01 - Combine ground flaxseed and water in a small bowl and let thicken for 5 minutes.
02 - In a large bowl, mash black beans with a fork or potato masher, keeping some texture.
03 - Add diced onion, bell pepper, garlic, oats, breadcrumbs, flax egg, smoked paprika, cumin, chili powder, salt, and pepper to the beans; mix thoroughly.
04 - Divide the mixture into four equal portions and shape each into a patty.
05 - Heat olive oil in a nonstick skillet over medium heat and cook patties 4–5 minutes per side until golden and heated through.
06 - Combine vegan mayonnaise, minced chipotle peppers, adobo sauce, lime juice, and salt in a small bowl; stir until well blended.
07 - Toast the burger buns if desired.
08 - Spread chipotle mayo on buns, then layer lettuce, tomato, onion, black bean patty, and avocado slices; top with remaining bun and serve immediately.