Method:
Ingredient Option: Use ground buffalo instead of ground beef.
In a medium bowl, thoroughly combine onion, horseradish, garlic, salt and pepper. Add the beef and lightly combine, taking care not to overwork the meat. With dampened hands, form the meat into 4 patties of even thickness. (These are fairly large patties; feel free to make 6 smaller patties if desired.) Make a large depression in the top of the patties, about 2 inches wide. Place a quarter of the cubed cheddar cheese in each depression and bring the meat over the cheese, enclosing it completely.
Place on a lined baking sheet, cover loosely with plastic wrap and chill for 30 minutes.
Meanwhile, light the grill or preheat the broiler. Cook the burgers for 4 to 5 minutes on each side, until done to your liking.