How to Make It
In a medium skillet, heat the 2 tablespoons of vegetable oil. Add the onion and garlic and cook over moderate heat just until softened, about 3 minutes. Add the cumin and cayenne and cook until fragrant, about 1 minute. Scrape the onion mixture into the bowl of a food processor. Add 1 1/2 cups of the beans and pulse until the mixture is finely chopped but not smooth. Scrape the mixture into a medium bowl. Mix in the remaining whole beans and 1/2 cup of the bread crumbs and season with salt and pepper. Form the mixture into twelve 1/4-cup patties, about 1/2 inch thick.
Put the flour, beaten eggs and the remaining 3/4 cup of bread crumbs into 3 shallow bowls. Dust each black bean cake with the flour, tapping off the excess. Dip the cakes in the egg and then in the bread crumbs, pressing so that the bread crumbs adhere.
In a very large skillet, heat 1/8 inch of oil until shimmering. Add the cakes and fry over moderate heat until golden brown, about 2 minutes per side. Drain on paper towels. Serve the black bean cakes with sour cream, avocado, scallions and lime wedges.