How to Make It
MAKE THE CHITARRA On a clean work surface, combine the flours and make a mound. Make a well in the center and break the eggs into the well. Beat the eggs lightly with a fork to break them up. Begin incorporating the flour with the fork. Once the mixture is too thick to mix, switch to your hands and start kneading. Continue to knead until you have incorporated all of the flour, or enough to make a stiff ball of dough. Knead for a few minutes more, until the dough is smooth. Wrap the dough tightly in plastic wrap and let rest for 30 minutes at room temperature.
Line a large rimmed baking sheet with clean kitchen towels and sprinkle with semolina flour. Cut the dough into quarters and roll each quarter into a 1/8-inch thick sheet. Using a traditional chitarra, trimming the sheets of pasta so they are 2 inches shorter than the length of the instrument. Place one sheet on the chitarra and using a small rolling pin, roll back and forth over the dough, pressing, first gently and then more firmly as you go, to cut through the dough. A wood slat in the bottom of the chitarra will catch the noodles as they fall through the wires. Tip out the noodles, sprinkle them liberally with semolina and wrap them around your hand to form a nest. If cutting by hand, cut each sheet into 1/4-inch thick strips and form a nest with the cut noodles. Cut the remaining sheets of pasta in the same way and set them on the prepared baking sheet.
MAKE THE ROASTED TOMATOES Preheat the oven to 375°. On a large rimmed baking sheet, toss the tomatoes and garlic with 2 tablespoons of the extra-virgin olive oil and season with salt and pepper. Roast until the tomatoes begin to brown and are juicy, about 25 minutes. Peel the garlic.
In a 12-inch skillet, heat the remaining 2 tablespoons of extra-virgin olive oil with the Calabrian chiles over moderate heat for 2 minutes. Remove from the heat and add the torn basil leaves. Scrape the tomatoes, garlic and any pan juices into the skillet. Crush the tomatoes and garlic with a fork. Bring the roasted tomatoes to a simmer over moderately high heat and cook until the mixture reduces slightly, about 4 minutes.
In a large pot of salted boiling water, cook 1 pound of pasta until al dente, 3 to 4 minutes; reserve 1 cup of the pasta cooking water. Add the pasta to the tomatoes along with half of the reserved pasta cooking water and cook over moderately high heat, tossing, until saucy, about 3 minutes; add more pasta cooking water as needed. Season with salt and pepper.
Transfer the pasta and tomatoes to 4 plates. Top with the stracciatella and basil leaves. Drizzle with green fruity olive oil and serve.