Heat the oven to 375°F. Lightly grease a 12-cup muffin pan.
In a large bowl, combine the ground beef, breadcrumbs, egg, mashed black beans, salsa, 1/4 cup of the cheddar, cumin, chili powder, salt, and black pepper. Mix gently until evenly combined, taking care not to overwork the meat.
Divide the mixture among 8 muffin cups, filling each about three-quarters full. Gently press the tops to make them level.
Bake for 20 minutes, then sprinkle the remaining 1/4 cup cheddar over the muffins. Return the pan to the oven and bake for about 5 to 10 minutes more, until the beef is cooked through.
Let the muffins rest in the pan for 5 minutes before removing them. Serve with extra salsa.