Heat butter in nonstick skillet over medium heat. Add mushrooms and onion; cook and stir 4 minutes or until mushrooms have softened. Cool completely.
Mix ground beef and Hamburger Seasoning. Measure twelve (1/4 cup) portions of beef. Shape into thin 4-inch round patties. Place about 1 tablespoon each of the mushroom mixture and cheese in center of each of 6 patties. Top with remaining hamburger patties, pinching edges to seal filling. If necessary, lightly flatten with spatula.
Grill over medium heat 4 to 6 minutes per side or until burgers are cooked through (internal temperature of 160°F). Serve burgers on toasted rolls with desired toppings and condiments.