Heat gas or charcoal grill to medium heat.
In 12-inch nonstick skillet, melt butter over medium-high heat. Add mushrooms, soy sauce and garlic; cook until mushrooms are tender and liquid evaporates. Set aside; keep warm.
Shape beef into 6 (1/2 inch thick) patties. Sprinkle with garlic powder, salt and pepper. Place patties on grill; cover grill. Cook with medium heat 8 to 10 minutes, turning once, until meat thermometer inserted in center of patties reads 160°F. Place cheese slices on top of burgers; cover and cook 1 to 2 minutes longer or until cheese is melted.
Place burgers in buns. Divide cooked mushrooms evenly over burgers. Top with tomatoes and onion.