1. Put the beans in a large bowl and cover with water by 3 or 4 inches; they will triple in volume. Soak for 24 hours, adding water if needed to keep beans submerged.
2. Drain beans well (reserve soaking water) and transfer to a food processor. Add remaining ingredients except oil; pulse until minced but not pureed, scraping sides of bowl down; add soaking water if necessary to allow machine to do its work, but no more than 1 or 2 tablespoons. Keep pulsing until mixture comes together. Taste, adding salt, pepper, cayenne or lemon juice to taste.
3. Put the oil in a large, deep saucepan to a depth of at least 2 inches; more is better. The narrower the saucepan the less oil you need, but the more oil you use the more patties you can cook at a time. Turn heat to medium-high and heat oil to about 350 degrees (a pinch of batter will sizzle immediately).
4. Scoop heaping tablespoons of batter and shape into balls or small patties. Fry in batches, without crowding, until nicely browned, turning as necessary; total cooking time will be less than 5 minutes. Serve hot or at room temperature
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