Place beets, onions and mushrooms in a food processor and pulse until roughly chopped. Add the black beans and pulse until the mixture is well-combined and small chunks of beans remain.
Transfer the mixture to a mixing bowl and add the egg, breadcrumbs, Worcestershire sauce, garlic salt, onion powder, and pepper. Mix well. Roll the mixture into six large patties or eight medium patties.
On a cast iron or skillet, over medium heat, grill the burgers for 5-7 minutes per side until the center of the patties feel firm.