Thinly slice the onion, bell pepper and mushrooms. Sauté in oil until everything is barely golden and is slightly wilted. Season well with salt and pepper. Place in a bowl. Form the ground beef into 4 patties and season. Fry the patties in oil for 4 minutes on each side. Now add the sautéed vegetables and, finally, top each patty with a slice of Castello Tickler Mature cheddar. Put the pan in a preheated oven until the cheese has melted. Alternatively, use a pan with high sides and cover with a lid.
Spread the warm buns with mayonnaise. Then top with lettuce, the patty and veggies and then the top bun.