In a food processor, pulse the beans until coarsely chopped, then transfer to a large mixing bowl. Pulse the walnuts in the food processor until finely chopped, then transfer to the mixing bowl with the beans. Add the breadcrumbs, salt, onion powder, garlic powder, pepper, egg and 2 tablespoons of the BBQ sauce and mix well. Divide the mixture into 4 equal parts. Shape into burger patties and refrigerate for 30 minutes.
Heat a nonstick skillet over medium-high heat. Add the olive oil. Brush the top of each burger with the remaining 1 tablespoon BBQ sauce. Cook the burgers BBQ sauce-side down for 3 minutes. Flip and top each with a slice of cheese if using. Cover and cook until the cheese is melted and the burgers are heated through, about 3 minutes. Place the burgers on the buns and top with desired toppings.