Start with 2 15.5-oz. cans black beans, drained. Add to the bowl of a food processor with ¼ cup bread crumbs, 1 large egg, 1 teaspoon each smoked paprika, cumin, salt, and pepper, and ¼ teaspoon cayenne. Pulse a couple times to combine. Firmly pack into 5 1-inch thick patties, transfer to a parchment-lined baking sheet, and refrigerate for 30 minutes. Heat oil in a skillet over medium. Cook patties, pressing gently with a spatula, until brown on both sides, about 6 minutes per side. Serve on buns with your choice of toppings.