Drain, but do not rinse, the black beans. Place them in a bowl and use a fork to mash them. Keep mashing until they're mostly broken up, but still have some whole beans visible. Add the breadcrumbs, onion, egg, chili powder, salt, pepper, and hot sauce. Stir until everything is combined, then let the mixture sit for 5 minutes. Heat a tablespoon or two of olive oil with an equal amount of butter in a skillet over medium-low heat. Form the bean mixture into patties slightly larger than the buns you're using (the patties will not shrink when they cook.) Place the patties in the skillet and cook them about 5 minutes on the first side. Flip them to the other side, place 2 slices of cheese onto each patty, and continue cooking them for another 5 minutes, or until the burgers are heated through. (Place a lid on the skillet to help the cheese melt if needed.)Grill the buns on a griddle with a little butter until golden. Spread the buns with mayonnaise and hot sauce, then place the patties on the buns. Top with lettuce and tomato, then pop on the lids!Yum.