Place a pan with the lamb chops in the center of the broiler rack. Dot the chops with butter and sprinkle with salt and pepper. Place as near the broiling unit as possible and broil until about half done, about 6 minutes. Remove the pan from the oven. Turn over the chops and dot with butter, salt and pepper. Put 4 pineapple slices dipped in melted butter around the chops, and in the center of each pineapple slice, place a large mushroom cap dipped in melted butter. Place tomato halves sprinkled with salt and pepper between the pineapple slices, return to the oven and complete broiling. Just before taking out the pan, sprinkle the tomatoes with grated cheese and basil.