Remove the lamb from the refrigerator 20 minutes before cooking. Pat dry thoroughly with paper towels, then season evenly with salt and black pepper.
Heat the olive oil in a large cast-iron skillet over medium-high heat until shimmering.
Place the chops in the skillet and sear for 3 to 4 minutes on the first side until a deep brown crust forms.
Flip the meat. Immediately add the butter, minced garlic, and chopped rosemary to the skillet.
As the butter melts, tilt the pan slightly and use a spoon to continuously baste the chops with the herb butter for 3 to 4 minutes, or until the internal temperature reaches 135°F for medium-rare.
Transfer the cooked meat to a plate, pour the remaining pan juices over the top, and let rest for 5 minutes. Garnish with fresh parsley before serving.