When stuffing the burgers, make sure to seal them well so that the melting cheese won't run out onto the grill while they're cooking. You can also use ground buffalo (bison) meat in place of the beef, if you like.
4 ounces sharp cheddar cheese, cut into 1/4-inch cubes
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.
Preheat the broiler or prepare a grill for cooking. Cook the burgers for 4 to 5 minutes on each side, until done to your liking.
Per Serving:490 calories (310 from fat), 35g total fat, 16g saturated fat, 145mg cholesterol, 580mg sodium, 3g carbohydrates, 39g protein.