Mash the beans in a large bowl with a fork. Add the breadcrumbs, ½ cup salsa, egg, garlic powder, onion powder, and cumin. Shape the mixture into 4 equal-sized patties and refrigerate for 30 minutes.
Heat the oil in a large skillet over medium heat. Cook the burgers for 5-7 minutes per side or until crispy on the outside and firm.
Spread top and bottom buns with mayonnaise. Serve on buns with remaining salsa, cilantro, and avocado slices.