In a large bowl, mash 1 cup beans; set aside.
In a food processor, combine remaining 2 cups beans, jalapeños, salsa, cumin and chili powder. Process until mixture becomes a paste. Transfer to large bowl with mashed beans; add bread crumbs and stir until well combined. Salt and pepper to taste. Form into 6 patties.
In a large skillet, heat oil over medium-high heat. Add burgers; cook until browned on both sides (about 8 minutes).
Meanwhile, in a small bowl smash avocado; add mayonnaise and mix until well combined. Divide evenly among hamburger buns; top with burgers, lettuce and tomato.