In a large bowl, mash the beans with a potato masher or fork until they are mostly smooth. Add the egg, breadcrumbs, cheese, oregano, and pepper. Stir to thoroughly combine. Shape into 4 even patties, about 1/2-inch thick. Coat both sides of the burgers with cooking spray.
Heat grill to medium-high. Grill until cooked through (160°F), about 4 minutes per side. Serve on buns with lettuce, tomato, and red onion slices.
