Add all ingredients to food processor and pulse until ingredients are mixed. Oil your hands, and form 4 burgers.
Place burgers on grill on high for 5-7 minutes or until you see grill marks. Flip the burgers and reduce heat to medium and add mushrooms to grill. Add cheese to top of burgers. Place lid on grill. Cook for an additional 8-10 minutes, flipping the mushrooms occasionally.