Mashed kidney beans are amped up with carrots, chili powder, and oregano for these meatless burgers.
Lightly mash beans in a large bowl, leaving some whole. Add carrot, chili powder, oregano, breadcrumbs, and eggs. Season generously with salt and pepper; stir until thoroughly combined. Divide mixture into 4 portions and form into patties.
Heat 2 tablespoons oil in a large nonstick skillet over medium heat. Add patties and cook, undisturbed, until bottom forms a browned crust and most of oil is absorbed, 10 to 12 minutes. Flip patties and add remaining 1 tablespoon oil to pan, swirling to coat bottom. Cook, undisturbed, until browned on other side and heated through, 8 to 10 minutes. Serve on buns with accompaniments.
The patties can be prepared through step 1 a day ahead, placed on a parchment-lined baking sheet, covered, and kept in the refrigerator.
For smaller appetites, form the bean mixture into six patties.