Oklahoma Fried Onion Burgers

Ingredients

• 1 large onion, peeled, halved and thinly sliced
• salt and pepper
• 1 lb ground beef
• 1 tablespoon butter
• 1 tablespoon vegetable oil
• 4-8 slices American cheese
• Mayo, mustard and pickles, for serving
• 4 hamburger buns, toasted