On cutting board, remove all the fat and gristle from sirloin. Marinate by spreading mustard and garlic over top. Add Worcestershire sauce, black pepper and salt. Let the meat marinate at room temperature for at least one hour (but not more that 2). When ready to cook, start barbecue and let it warm up for about ten minutes. Place the beef on the grill. Cook for 8 minutes per side, (medium rare) or until the beef is done to your taste. Transfer beef to carving board, using barbecue tongs. Carve the beef by slicing across the grain into strips 1/4-inch thick. At the same time that you transfer the beef, start toasting the white sandwich bread. Slice the bread into 3 strips and place on serving platter. Arrange beef on top of sliced bread.
In a saucepan on the grill, heat unsalted butter. Add Worcestershire sauce, garlic, wine, pepper, salt and, whisking constantly, cook over medium heat for about 5 minutes. Remove saucepan from grill and spoon the sauce over the beef and bread. Serve immediately. Must eat while hot, and must be eaten using your fingers.