Heat olive oil in a cast iron or stainless steel skillet over medium-high heat. Pat the lamb chops dry using paper towels.
Season both sides of the lamb chops generously with salt and black pepper.
Once the pan is hot, place the lamb chops in the skillet and sear for about 2 minutes per side until a golden crust forms. Remove the chops from the pan and set aside.
Reduce heat to medium-low. Add minced garlic to the same pan and cook for about 1 minute until fragrant.
Whisk in brown sugar, balsamic vinegar, cayenne pepper, and a pinch of salt and pepper. Allow the sauce to simmer and thicken slightly.
Return the lamb chops to the pan and spoon the sauce over them continuously.
Continue cooking the Balsamic Lamb Chops until they reach your preferred doneness:
125–130°F for medium-rare
135°F for medium
Remove from the pan and let the lamb chops rest for about 5 minutes.
Garnish with fresh parsley and serve warm.