Drain the black beans, but do not rinse them.
Put the beans in a bowl and use a fork to mash them. Mash them until they are mostly mashed, but some whole beans are still visible.
Add the breadcrumbs, onion, egg, chili powder, salt, and pepper.
Stir until everything is combined, then let the mixture sit for 5 minutes.
Heat two tablespoons of olive oil and two tablespoons of butter in a skillet over medium-low heat.
Form the bean mixture into patties slightly larger than the buns you're using. These patties won't shrink when you cook them.
Place gently in the pan and cook for about 5 minutes on the first side.
Turn the patties over gently and cook for another 2 minutes on the other side.
Add your cheese to each patty, and continue cooking for another 4-5 minutes.
Place patties on buns and top with your favorite burger fixin's.