Slice plantains diagonally and coat them in the cinnamon sugar mix and set aside.
Heat cast-iron skillet over high heat, then pour in ½ cup vegetable oil. Fry plantains until warm brown in colour and fully cooked through.
Remove hot pan and wipe out debris. Add 2 tablespoon oil and fry the eggs in a 3 inch wide cookie ring (optional) just until the whites are cooked leaving the yolk runny (or fully cook eggs if desired) set eggs aside on a plate.
Cook the beef patties according to package instructions. While in the pan top with 1 slice of cheese sprinkle a bit of water to create steam to help the cheese to melt faster. Set aside.
Build the burgers by placing each cooked patty on the bottom bun (smothered with about 1 tsp of mayo). Top with the egg, then cinnamon sugared plantains, lettuce and tomatoes. Serve bacon on sides.