In a heavy grill pan preheated over medium high heat, add the chops and season with salt and pepper along with 1/2 teaspoon oregano. Cook chops and mushrooms for 5 minutes on each side.
Transfer cooked lamb and mushrooms to a heated ovenproof plate and add cheese. Preheat the oven grill and grill until the cheese is cooked and bubbling. Serve with crusty white bread.