01 - In a small bowl, combine ground flaxseed and water; let rest for 5 minutes to thicken.
02 - Pulse rolled oats in a food processor until a coarse meal forms.
03 - Add black beans, red onion, cilantro, garlic, tomato paste, cumin, smoked paprika, salt, pepper, and flax egg to oats; pulse until combined yet slightly chunky.
04 - Shape the mixture into 4 even patties.
05 - Heat olive oil in a large skillet over medium heat; cook patties 4 to 5 minutes per side until browned and heated through.
06 - In a small bowl, mix vegan mayonnaise, minced chipotle peppers, adobo sauce, lime juice, and salt until smooth.
07 - Toast burger buns if preferred.
08 - Spread chipotle mayo on buns; layer with lettuce, tomato, red onion, black bean patty, and vegan cheese if using; top with remaining bun halves.
09 - Serve burgers immediately while warm.