Place oil in a skillet and cook the onion slices on medium low heat until caramelized all over. Remove to drain on a paper towel.
Make two oval patties and season with salt and pepper. Fry in same skillet until done.
Take one tsp of mayo and spread on the outside of each slice of bread. Top each with burger onions and 2 pieces of cheese each. Fry the sandwich about 3 minutes on each side until browned and cheese is melted