Instructions

Adjust oven rack to middle position and heat oven to 475 degrees. Pat pork dry with paper towels and season with salt and pepper. Heat 1 tablespoon oil in 12-inch skillet over medium-high heat until just smoking. Add pork and cook until well browned on 1 side, about 5 minutes. Flip pork, transfer skillet to oven, and roast until pork registers 145 degrees, 5 to 7 minutes. Transfer pork to carving board, tent with aluminum foil, and let rest while preparing sauce.
Return now-empty skillet to medium-high heat (skillet handle will be hot). Add remaining 2 tablespoons oil, onion, and ½ teaspoon salt and cook until onion is just beginning to soften, about 2 minutes. Stir in tomato paste, garlic, and thyme and cook until rust-colored and fragrant, about 2 minutes. Stir in tomatoes and their juice and broth; bring to boil. Reduce heat to medium-low and simmer until thickened, 5 to 7 minutes. Off heat, stir in capers. Season with salt and pepper to taste. Cut pork into ½-inch thick slices, transfer to platter, and pour sauce over top. Serve.