Season lamb with salt and pepper and leave at room temperature for up to two hours, or refrigerate for up to 8 hours (bring to room temperature before cooking). In a small bowl, mix together rum, lime juice and honey, then set aside.
Place a heavy skillet (not nonstick, and large enough to hold 6 lamb chops in a single layer) over medium-high heat. Coat with oil and, when hot, add 6 chops. Cook to an internal temperature of 125°F for medium-rare (timing will depend on thickness of lamb, but usually no more than 3 minutes per side). Remove lamb to a platter, tent with foil, and repeat with remaining 6 chops.
While lamb rests, add shallots to the hot pan and cook until translucent and starting to brown, about 30 seconds. Add rum mixture, scraping up brown bits, and let boil until it thickens to a sauce consistency, about 2 minutes. Turn off heat and add mint and butter, stirring until butter melts. Taste and add salt, if needed.
Using tongs, drag chops through the sauce to coat. Serve immediately. Serves 4
