1. In a small microwave-safe bowl or glass measuring cup, combine 2 tablespoons chicken broth and mustard seeds. Heat in a microwave oven on full power (100%) until bubbling, 15 to 30 seconds. Pour into a large bowl and add remaining 1/4 cup broth.
2. Add ground beef, bread crumbs, egg, and salt; mix well.
3. Divide beef mixture into four equal portions; shape each into an evenly thick 4-inch-wide round. Wrap a slice of bacon snugly in a ring around edge of each patty, overlapping ends and securing with a toothpick. If making ahead, lay patties in a single layer on a plate, cover airtight, and chill up to 1 day.
4. Lay beef patties on a lightly oiled barbecue grill over a solid bed of medium coals or medium heat on a gas grill (you can hold your hand at grill level only 4 to 5 seconds); cover barbecue and open vents. Cook patties until browned on the bottom, 4 to 6 minutes. Turn with a wide spatula and continue to cook until patties feel firm when pressed and are no longer pink in the center (cut to test), 4 to 7 minutes longer. Cover meat evenly with cheese and lay buns, cut side down, on grill; cover and cook until cheese is melted and buns are toasted, 2 to 3 minutes.
5. Spread toasted sides of each bun with mayonnaise. Set a beef patty on each bun bottom. Pull out toothpicks and discard. Top each with horseradish slaw and cover with bun top.
Horseradish slaw: In a blender or in a bowl with a fork, mix 1/4 cup cream cheese or Neufchâtel (light cream) cheese with 3 tablespoons fat-skimmed chicken broth, 2 tablespoons prepared horseradish, and 1 tablespoon lemon juice. In a bowl, mix horseradish dressing with 3 cups finely shredded cabbage (8 oz.; sometimes labeled angel hair), 1 tablespoon minced onion, and salt and pepper to taste. If making ahead, cover and chill up to 1 day; mix before serving. Makes 1 1/2 cups.