In a skillet with butter sauté onion and peppers for about 5-8 minutes, until tender.
In a large bowl, mix together the ground beef with the A1 sauce, egg, bread crumbs, salt, and pepper. Add the sautéed onions and bell pepper.
Mix until completely combined then evenly separate the meat mixture into four equal parts. Form into patties.
Use a cast iron fry pan to cook to the desired doneness (120 F for rare, 130 F for medium rare, and 160 F for well-done). Top with cheese and let the cheese melt for 1-2 minutes.
Remove the patties from the grill and place them on the plate. Butter the pretzel rolls and place them in the hot pan to toast for about one minute. Place burgers on pretzel rolls and top with favorite toppings.