Combine meat and ketchup. Form into 12 balls and flatten into small burgers.
Heat large skillet over medium-high. Add burgers and cook until well-browned on both sides. Remove burgers from skillet. Pour off any fat.
Add drained onions and peppers to the skillet and heat to a simmer. Place burgers back into skillet. Reduce the heat to low. Cover and cook for 1-2 minutes or until desired doneness
Top the burgers with the cheese if desired and cook until the cheese is melted. To serve, spread bottom of buns with a little coarse ground mustard and place the burgers on the buns and top each with 1 heaping tablespoon of carmelized onions and peppers.