1. In a food processor fitted with a metal blade, place onion, garlic, and cumin; pulse until coarsely chopped. Add beans, bread crumbs, and cilantro; pulse until just combined (dont puree). Transfer mixture to a bowl; stir in walnuts. Season with salt and pepper. Fold in egg and stir until combined. Form into four 31/2-inch patties. (If burgers seem very wet, add 1/4 cup bread crumbs.) Chill patties, covered, at least 1 hour, and up to 1 day.
2. Meanwhile, in a small bowl, stir together salsa ingredients. Add salt to taste. Set aside. Peel, pit, and mash avocados in a medium bowl with juice and salt to taste. Cover the surface of the avocado with plastic wrap to seal out air. Set aside.
3. In a large skillet, heat oil over medium heat until hot; cook patties until light brown, 4 to 6 minutes on each side. Toast muffins. Place a spoonful of guacamole on muffin bottom; add a burger, some salsa, a muffin top, and serve.