Four generations of the Huneeus family give Easter a Latin accent with pork empanadas and herb-crusted lamb, all matched with their phenomenal (and inexpensive) wines.

In Chilean wine, the Huneeus name is as famous as Mondavi is in the United States. Since the 1960s, the winemaking family behind the Veramonte label has helped turn Chile into a powerhouse of dependable, inexpensive reds, and more recently, they have pioneered fine single-estate blends in California. Now, as four generations gather for Easter at patriarch Agustin "Cucho" Huneeus and his wife Valeria’s house in the glamorous beach town of Zapallar, Chile, the family discusses its new mission: to show the world that inexpensive Chilean wine can be better than dependable—in fact, it can be stellar.

The day begins with an Easter egg hunt, organized by Valeria. After the granddaughters have searched and screamed through the house—an 1890s adobe villa with an inner courtyard full of hydrangeas, calla lilies and jacaranda trees—the family gathers in the front garden for an Easter feast. At a table overlooking a cove filled with red and blue fishing boats, Agustin Sr. and his son Agustin Francisco pour the wine. Delicate shooters of local king crab and sweet avocado are delicious with a crisp Veramonte Sauvignon Blanc. The main course is a juicy leg of lamb encrusted with bread crumbs, mustard and fresh herbs; it’s matched with Primus, Veramonte’s signature blend of Merlot, Cabernet Sauvignon and Chile’s Carmenère. Valeria, who is a vegetarian, serves the lamb alongside crispy, puffy potato balls (papas duquesas) and a traditional Chilean tomato salad with sweet onions. "I always cook a meat because I cannot impose myself," she says in a voice that is both regal and breathy.

The Veramonte vineyards are in Casablanca Valley, 45 minutes northwest of Santiago. Not long ago, the area was nothing but pasture and scrub forest, and unlike the majority of Chile’s wine areas, it does not get water runoff from the Andes. Agustin Sr. bought land there in 1990 after noting the distinctive flavor of grapes from a small local vineyard. "When my father made his investment here, Casablanca didn’t exist," says Agustin Jr. "People thought he was insane." Because of its long, cool growing season, the valley is now a prized appellation—Casa Lapostolle and Concha y Toro both have vineyards there—producing richer, though far fewer, grapes than Chile’s warmer Central Valley. "We can hold off on picking the grapes to make the tannins smoother without losing fruit flavor," says Veramonte winemaker Rafael Tirado. The winery building—imagined by Agustin Sr. as a replica of Santiago’s central market, which was designed by Gustave Eiffel—is surrounded by 1,100 carefully planted acres of the Chardonnay, Sauvignon Blanc, Cabernet Sauvignon, Merlot and Carmenère grapes that become 200,000 cases of Veramonte and Primus wine each year.

The 73-year-old Agustin Sr. is a hands-on vintner whose closest encounter with retirement is a daily post-lunch siesta. As we walk through Chardonnay vines that have just been pruned, he stops and calls over Jorge Figueroa, Veramonte’s viticulturist, and points to bunches of grapes on the ground. "What’s your strategy with this?" he asks. Figueroa explains that they’ve cut the grapes to keep production to no more than seven tons per hectare in keeping with Agustin Sr.’s mandate of quality over quantity. As his father nods, Agustin Jr. says, "He hates that there are so many grapes on the ground. This is a lot of money."

Agustin Sr., who combines an aristocratic bearing with hand-on-your-back bonhomie, is a descendent of one of Chile’s oldest families. His ancestors include the first president of the University of Chile and the wife of the founder of the legendary Concha y Toro winery. He has lived in both the United States and Argentina, where he fled after the election of President Salvador Allende. "Agustin and Valeria have traveled all over, so they have a vision of the world that is different from other people in Chile, who have been limited by geography," says writer Isabel Allende, the niece of the former president and, ironically, one of Agustin Sr.’s closest friends.

Agustin Sr.’s life swerved into wine in 1960, while he was managing his father’s fish meal company. As an investment, his stockbroker suggested he borrow money to buy the struggling Concha y Toro. He decided to change the wines from a commodity sold in bulk in just two varieties—red and white—into something more appealing. He improved quality, introduced new brands at different prices, and started selling wine in European-style bottles instead of caning-wrapped chuico jugs.

By the end of the 1960s, Concha y Toro was exporting $1 million worth of wine a year. That ended with the 1970 election of Allende, whose socialist policies were at loggerheads with large landowners like Agustin Sr. Hearing rumors that he was about to be arrested, Agustin Sr. fled with his family to Buenos Aires. He eventually came to New York to head international operations for Seagram’s. Agustin Sr. left corporate life the day after he received his green card in 1977.

After Agustin Sr. bought and sold several California vineyards in the 1970s and ’80s, vintner Peter Sichel called him to help sell the flailing Franciscan Vineyards. Agustin Sr. ended up staying on as a partner and starting Franciscan’s Estancia label, which turned heads when, at $14 a bottle, it won the 1991 Sonoma County Harvest Fair’s Sweepstakes Award. "There had been no real demand for quality wines at $10 before, and what came afterward—Kendall-Jackson and the like—started there," says Agustin Jr. The Huneeuses entered the high-end California market in the early 1990s after buying a Napa vineyard that now turns out a single wine: Quintessa, an opulent blend of Cabernet Sauvignon and Merlot that currently commands $125 a bottle.

Veramonte, like Quintessa, illustrates the potential of single-estate blends. A pioneer of this Meritage concept, Agustin Sr. says, "I don’t think for a minute that the variety of the grape defines the wine." One of the purest expressions of this is the robust, berry-flavored $20 Primus, launched in 1997. "Chile’s role is to make $20 wines better than any other place in the world," says Agustin Jr. "To do Primus in California, it would have to be a $100 wine."

With his mop of hair, bell-bottomed brown corduroys and MBA from Northwestern, 41-year-old Agustin Jr. is something of a foil to his Prada sunglasses-wearing father. Where Agustin Sr. is open and romantic, his son is intense and more businesslike, and what they call each other—Father and Augie—reflects this. After working on and off with his father throughout his life—one of his first memories is flying in his father’s plane over a vineyard, looking down on the grape pickers—Agustin Jr. came back to the family business in 2003. Says Valeria, "It wasn’t what I wanted, but I realized that it was what my son wanted. I always feared the electricity of the father-son relationship. But they work well." A self-described "finance guy" who reels in his father when he becomes too expansive ("Oh, Mr. Censor," Agustin Sr. responds with a smile), Agustin Jr. runs marketing and strategy while his father oversees planting and production. "As an MBA, Augie understands the business environment of wine today more than I do, since I got stuck in the ’romance’ part of the wine business," says Agustin Sr. In late 2007, Agustin Jr. will put his business acumen to the test with another venture: He will launch a boutique chocolate company based in San Francisco, sourcing the best cocoa from Venezuela.

Back at their Easter meal, Agustin Jr. is surrounded at the table by his three daughters—nine-year-old Antonia, seven-year-old Agustina and four-year-old Emilia—and his wife, Macarena, a clothing designer he met as a teenager. The family finishes their lunch with a delightful napoleon layered with flaky phyllo pastry, pillows of pastry cream and the delicious Latin American caramel called dulce de leche. While the girls scamper off in search of more Easter eggs, Agustins Sr. and Jr. talk about the future of Veramonte. They’re searching the best plots for what Agustin Jr. thinks is next: Pinot Noir. "Looking for the destiny of the land, that’s exciting," Agustin Sr. says, his voice dreamy. "There’s some land out there that’s our future. We have to explore. So we’ll have to build a road." His son sighs. "Great," he murmurs. "Because we’re so good at that."

Ian Mount has written for the New York Times, Wall Street Journal and New York Magazine. He lives in Buenos Aires.