Heat the olive oil over medium heat. Sauté the onion and garlic, stirring occasionally, for 8-10 minutes, until soft and fragrant. Stir in 2 cups of the beans, then add the cumin, paprika, chili powder, salt, and pepper. Sauté until heated through.
Preheat oven to 350˚F.
Transfer the bean mixture to the bowl of a food processor along with the bread crumbs. Pulse until well combined, but still has texture. Don't let it turn mushy. Transfer the mixture to a large bowl. Fold in the last cup of beans and the corn, using your hands, if necessary, to incorporate. Taste, and adjust seasoning if needed.
Shape the mixture into 4 large (or 6 smaller) patties. If the patties are not holding together, add a bit more breadcrumbs. Arrange the burgers on a baking sheet, and bake for 30-35 minutes, until golden, flipping once halfway through. Serve on toasted buns with your favorite toppings.