How to Make It
In a small nonreactive saucepan, combine the onion, balsamic and sherry vinegars, sugar and 1/4 teaspoon of cracked black pepper and bring to a boil over high heat. Reduce the heat to moderately low and cook, stirring occasionally, until the liquid is reduced to a thick syrup and the onions are soft, about 30 minutes. Serve the marmalade chilled or at room temperature. Meanwhile, preheat the oven to 425°.
In a medium saucepan, cook the broth over high heat until reduced to 1 cup, 10 to 15 minutes.
In a large ovenproof skillet, melt 1 tablespoon of the butter in the olive oil over moderately high heat. When the foam subsides, season the pork lightly with pepper and cook in the skillet until browned on 3 sides, about 2 minutes per side. Transfer the pan to the oven and roast the meat for 8 to 9 minutes, or until an instant-read thermometer inserted in the thickest part reads 135°. Transfer the pork to a cutting board; let rest while you finish the sauce.
Meanwhile, discard the fat in the skillet and return the pan to high heat. Add the reduced broth and boil over high heat, scraping up any brown bits from the bottom of the pan, until reduced to 1/4 cup, about 6 minutes. Off the heat, whisk in the remaining 3 tablespoons of butter. Season with salt.
Slice the tenderloin across the grain and arrange on 4 plates. Spoon some of the onion marmalade next to the pork, drizzle with the pan sauce and serve.