Place pepper on plate and press each chop firmly into pepper so that it adheres to the meat. Heat oil in 2 large skillets over high heat. Add peppered chops and sear quickly on both sides. Sprinkle chops with salt. Reduce heat to medium. Do not degrease the pan. Add stock and lime juice and continue to cook until the chops reach the desired doneness, about 2 minutes for medium rare. Remove chops to a plate and keep warm in a 200 degree oven.
If you are using the dried tarragon, add it now to the skillets and continue to cook until liquid reduces to a shiny glaze. Remove from heat. Wisk in butter. Add grated lime peel and fresh tarragon it that is what you are using. Remove chops from the oven to a warm platter. Add any lamb juices to the sauce. Spoon sauce over chops and serve.