Combine 2 cups of the beans with the bell pepper, onion, cilantro and spices in a large bowl.
Puree the remaining half a cup of black beans with the egg white in the food processor.
Mix the puree into the other ingredients while mashing it together. Sprinkle the cornmeal over the black bean mixture and work it in.
Shape the mixture into six patties (4 if you want larger burgers).
Heat the oil in a large nonstick skillet until shimmering. Carefully add patties to skillet. Cook the patties until they are brown and crispy on the bottom about 5 to 6 minutes flip and cook the other side for 5 minutes.
While cooking combine the chipotle adobe sauce with the sour cream, mayo and lime.
Top burgers with Monterey Jack cheese and avocado.