Preheat a grill or broiler until quite hot and put the rack no more than 4 inches from the heat source.
Put the butter in a small saucepan and turn the heat to medium; when the butter melts and its foam begins to subside, add the shallot and cook until soft, stirring occasionally, about 5 minutes. Add the vinegar, stir, and cook until it is just about evaporated, 1 or 2 minutes. Turn the heat to low and stir in the cheese and the cayenne. Stir occasionally until the cheese melts, then taste and adjust the seasoning as necessary (the sauce probably won’t need any salt). Keep warm while you grill the steaks.
Season the steaks well with salt and pepper, then grill or broil them for 3 to 4 minutes per side for medium-rare, longer or shorter according to your taste. Serve the steaks with a spoonful or two of sauce over each, garnished with the parsley or chives if you like.
