Prior to cooking, let the lamb to rest on the counter for 20 minutes. Salt and pepper the lamb generously on both sides.
Cast iron skillet with olive oil heated over medium-high heat. A heated skillet is ideal. Please wait. For medium, sear for 4-5 minutes per side.
Add butter, garlic, and rosemary to the skillet's edge in the final two minutes of cooking. To allow the drippings, butter, herbs, and garlic to combine and sizzle, tilt the pan for a moment. When the chops are finished cooking, drizzle the butter and juices over them to add flavor. Before serving, remove from the pan and allow it rest for five minutes.