In a 3-quart saucepan, simmer the beans, onion, garlic, salt, and water, covered, until the beans are tender- about 8 minutes. Stir in the cilantro and parsley and let it stand, uncovered, for 5 minutes.
Drain the bean mixture in a sieve and transfer to a food processor. Add the cumin, cayenne, 3 tablespoons of lemon juice, 4 tablespoons of oil, dill and mint; purée until smooth. Transfer to a bowl and cool to room temperature, stirring occasionally. Season with salt and pepper and add additional lemon juice to taste. Taste again, and add additional cumin or cayenne, if needed.
Mound the dip in a serving bowl and drizzle with the remaining tablespoon of oil. Serve with toasted pita wedges and/or fresh cut vegetables.
Notes
Make ahead tip: Prepare and cover. Dip will keep well in refrigerator for up to 3 days.