Slice Redi-Burger into 8 equal patties. Spray non-stick skillet with cooking spray and fry Redi-Burger over medium heat until lightly browned on each side (approx. 3 minutes on each side). Remove patties from skillet and sauté sliced onion in skillet until lightly browned. Add vegetable broth cover skillet. Steam onions until tender.
Assemble sandwiches by placing 1 slice of Redi-Burger and 1 slice of cheese on slice of rye bread. Top with onions and another slice of rye bread. Lightly butter outside surfaces of bread and fry in skillet over medium heat until both sides of bread are toasted and cheese has melted. Serve immediately.