On a small plate with a fork blend all ingredients together well and transfer to a sheet of wax paper. Using wax paper as an aid, shape butter into a 4-inch-long log and wrap. Chill butter 1 hour long, or until firm. Bèarnaise butter may be made 5 days ahead and kept chilled, wrapped tightly.
Prepare grill.
Bring steaks to room temperature and rub lightly with oil. Season steaks with salt and pepper and grill on a rack set 5 to 6 inches over glowing coals 4 to 5 minutes on each side for medium-rare meat. (Alternatively, steaks may be grilled in a hot well-seasoned ridged grill pan over moderately high heat.)
Serve steaks topped with slices of bèarnaise butter.
