In a large skillet, heat the butter over medium-high heat. Fry the chops in the butter for about 3 to 4 minutes, browning both sides. Remove from the pan and set aside.
Whisk the flour into the pan juices and cook for 2 to 3 minutes. Whisk in the broth and sherry, and then add capers salt, pepper and sugar. Bring slowly to a boil, stirring continuously. Reduce the heat until the sauce is at its simmering point.
Place the chops back into the pan. Cover with a lid and simmer on very low heat for about 5 more minutes- or until the temperature on a digital meat thermometer inserted into the meaty part of the lamb chops reaches 125°F for medium-rare. Remove the chops to a plate and cover with foil to rest for 5 to 10 minutes before serving.
Serve the lamb chops drizzled with sauce.
Notes
If you are preparing this recipe as gluten-free, just be sure to use an alternative thickener to the all-purpose flour, such as GF all-purpose flour, and be sure to use a brand of chicken broth that is known to be GF.