1. Mash black beans with a fork in a large bowl.
2. Mix carrots, onion, potatoes, and corn into the mashed beans.
3. Stir eggs into bean mixture to integrate completely.
4. Form the mixture into 8 patties with wet hands; season with salt and black pepper.
5. Heat vegetable oil in a skillet over medium heat. Cook the patties in hot oil until cooked through, about 6 minutes per side.