In a large bowl, combine egg and beer. Stir in bread crumbs, caraway seeds, marjoram, garlic, salt, and pepper. Add ground veal; mix well. Shape mixture into four 3/4-inch-thick patties.
For a charcoal grill, place patties on the rack of an uncovered grill directly over medium coals. Grill for 14 to 18 minutes or until done (160 degrees F), turning once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place patties on grill rack over heat. Cover and grill as above.)
When burgers are nearly done, add rye bread slices to the grill. Grill for 1 to 2 minutes or until bottoms are lightly browned. Turn bread slices; place cheese on four of the bread slices. Grill for 1 to 2 minutes more or until bottoms are lightly browned.
Place burgers on the cheese-topped bread slices. Spread the plain bread slices with mustard; place on top of burgers. Makes 4 servings.