01 - Combine ground flaxseed and water in a small bowl and let thicken for 5 minutes.
02 - In a large bowl, mash black beans until mostly smooth with some texture remaining.
03 - Add oats, breadcrumbs, red onion, garlic, flax egg, tomato paste, smoked paprika, cumin, chili powder, salt, and black pepper to the beans; stir until fully combined.
04 - Divide the mixture into four equal portions and shape each into a firm patty.
05 - Heat olive oil in a skillet over medium heat and cook patties for 5 to 6 minutes per side until browned and cooked through.
06 - Combine vegan mayonnaise, chopped chipotle peppers, adobo sauce, lime juice, and salt in a small bowl; mix well and adjust seasoning as needed.
07 - Toast burger buns if desired to enhance texture and flavor.
08 - Spread chipotle mayo on buns, place a black bean patty on each, and top with lettuce, tomato slices, red onion, and pickles; serve immediately.