Mash the black beans in a large bowl until most are broken down but some chunks remain. Stir in the breadcrumbs, onion, garlic, cumin, chili powder, egg, salt, and pepper until the mixture holds together.
Divide the mixture into four equal portions and shape each into a patty about 3/4 inch thick.
Heat the olive oil in a large skillet over medium heat. Cook the patties for 4 to 5 minutes per side until they are browned and heated through.
Transfer the cooked patties to a plate. Spoon the sour cream into a small zip-top bag, snip off one corner, and pipe a spiderweb pattern on each patty by drawing three concentric circles and then dragging lines outward from the center.
Top each patty with avocado slices and serve on buns if desired.