In bowl, beat egg and water with fork; mix in bread crumbs, onion, mustard, salt, Worcestershire and pepper.
Mix in beef.
Shape into four 1/2-inch (1 cm) thick patties. (Make-ahead: Cover and refrigerate for up to 6 hours. Or layer between waxed paper in airtight container and freeze for up to 1 month; thaw in refrigerator).
Place patties on greased grill over medium-high heat; close lid and cook, turning patties once, for about 10 minutes or until no longer pink inside.