Preheat a barbecue or stovetop grill to very hot. Combine beef, horseradish, garlic paste and herbs. Mix well and season with salt and pepper to taste. Divide mixture and form 2 firm, round, 3/4-inch thick patties. Place on hot grill and cook 5 minutes. Meanwhile, slice buns in half and brush with butter. Flip burgers and continue to cook 5 more minutes. Place buns, butter side down, on cooler part of grill and toast. Top each burger with a slice of cheese and continue to cook until cheese melts. Assemble burgers and serve them with fried potatoes.