In a saucepan, cover the beans with 2 inches of water. Simmer over moderately low heat, stirring occasionally, until tender, about 1 hour; add water as needed to keep the beans covered by 2 inches. When tender, season with salt, let set for 5 minutes and then drain.
Heat 1/2 tablespoon of the olive oil in saucepan. Add the farro and cook over moderately high heat, stirring, 2 minutes. Add 1 1/2 cups of water and a pinch of salt and bring to a boil. Cover and simmer until the grains are al dente, about 30 minutes.
In a small skillet, heat the remaining 3 tablespoons of olive oil. Add the diced onion and cook over moderate heat until softened. Add the crushed red pepper and garlic and cook for an additonal 2 minutes.
In a food processor, pulse all but 1/2 cup of the beans to a chunky puree; transfer to a bowl. Fold in the remaining 1/2 cup of beans, the farro, the onion mixture, eggs, bread crumbs, basil, cilantro, pepper and 1 teaspoon of salt. Form the mixture into 8 patties. Cover and refrigerate for 30 minutes.
In a large, nonstick skillet, heat 1/8 inch of vegetable oil. Add the burgers and cook over moderate heat, turning once, until browned and heated through, about 6 minutes. Transfer the burgers to the buns. Serve.