How to Make It
Season the lamb chops with salt and pepper. In a very large skillet, heat 2 tablespoons of the olive oil until shimmering. Add the lamb chops and cook over moderately high heat, turning once, until browned on the outside and medium-rare within, about 12 minutes. Transfer the lamb chops to a platter and keep warm.
Reduce the heat to moderate. Add the shallot to the skillet and cook until fragrant, about 30 seconds. Add the sherry vinegar and simmer for 1 minute, scraping up the browned bits from the bottom of the pan. Add the chicken broth and simmer until the sauce coats the back of a spoon, about 2 minutes. Stir in the piquillo peppers and capers and cook until warmed through. Remove the skillet from the heat and stir in the remaining 1 tablespoon of olive oil and the parsley; season with salt and pepper. Pour the sauce over the lamb chops and serve.