01 - Heat 1 tablespoon olive oil in a large skillet over medium heat. Add mushrooms, red onion, carrot, and corn. Cook, stirring occasionally, until vegetables are softened, about 5 to 7 minutes. Allow mixture to cool slightly.
02 - Place black beans in a large mixing bowl. Using a potato masher or fork, mash the beans until mostly smooth while retaining some chunks for texture.
03 - Add the sautéed vegetables to the mashed beans. Stir in rolled oats, breadcrumbs, egg or flax egg, soy sauce, smoked paprika, cumin, garlic powder, salt, and black pepper. Mix thoroughly until ingredients are well incorporated.
04 - Divide the mixture into 4 equal portions. Form each portion into patties approximately 1/2 inch thick.
05 - Heat the remaining 1 tablespoon olive oil in a nonstick skillet over medium heat. Place the formed patties in the skillet and cook for 5 to 6 minutes per side, or until golden brown and firm to the touch.
06 - Transfer cooked patties to buns and serve immediately with desired toppings such as lettuce, tomato, pickles, and sauces.