In a large bowl mix together the ground beef, egg, breadcrumbs, orange zest and salt. Form into 4 patties and press a dimple into the top of each one.
Heat a cast iron frying pan over medium high heat and toast the buns.
Lower the heat of the frying pan to medium and oil lightly. Cook the burgers 5 minutes each side for a well-done burger or 3 minutes per side for a medium-rare burger.
While the burgers are cooking, spread each bun with mayonnaise on top and bottom and garnish each with a few strips of red peppers and some arugula.
Place a patty on each bun and top with 2 cheese slices and the top half of the bun.
