Smoky Buffalo Burger

Name: Smoky Buffalo Burger
Ingredients: 2 tablespoons smoky barbecue sauce, divided; 1/4 cup low-fat mayonnaise; 3/4 teaspoon freshly ground pepper; 4 thin slices sweet onion, such as Vidalia; 1/2 cup shredded smoked cheese, such as Cheddar, Gouda or mozzarella; 1/4 teaspoon salt; 4 whole-wheat hamburger buns, toasted; 1 pound ground buffalo, (bison); 2 teaspoons prepared horseradish; 2 teaspoons Dijon mustard; 1 tablespoon paprika, preferably sweet Hungarian; 4 slices tomato; 1 tablespoon sweet pepper relish, or pickle relish; 1 teaspoon minced garlic; 1/2 cup cooked wild rice, (see Tip)