Heat the oil and butter in a frying pan over a medium heat, and add the chopped onion, green pepper and mushrooms. Cook for 5 minutes or so, until fairly soft, but still retaining a bit of bite.

Cut the burger buns in half, and toast lightly (either in a toaster, or in a dry frying pan). Spread one half of each bun with mayonnaise, and the other half with ketchup.

Distribute the sautéed vegetables between the three buns, and top each with two slices of American cheese. Finish with some lettuce leaves and sliced tomato (or your choice of additional toppings). Replace the lid of each bun, and wrap them in foil to serve, if desired.