01 - Combine ground flaxseed and water in a small bowl and let sit for 5 minutes to thicken.
02 - Pulse rolled oats in a food processor until they form a coarse meal.
03 - Add black beans, red onion, cilantro, garlic, tomato paste, cumin, smoked paprika, salt, pepper, and prepared flax egg to the food processor. Pulse until just combined, maintaining some texture.
04 - Shape the mixture into four equal-sized patties.
05 - Heat olive oil in a large skillet over medium heat. Cook patties for 4 to 5 minutes on each side until browned and heated through.
06 - In a small bowl, mix vegan mayo, minced chipotle peppers, adobo sauce, lime juice, and salt until smooth.
07 - Toast the burger buns if desired.
08 - Spread chipotle mayo on each bun. Layer with lettuce, tomato, onion, black bean patty, and vegan cheese if using. Top with the remaining bun.
09 - Serve the burgers immediately while warm.