Trim about 1/4 inch off the top of the garlic bulb, to expose the cloves; drizzle with 1 tablespoon olive oil and wrap in aluminum foil.
Bake in the preheated oven until soft, about 1 hour. Let cool until easily handled, about 10 minutes.
Squeeze roasted garlic cloves into a food processor. Add 1 tablespoon olive oil, edamame, cilantro, tahini, lemon juice, and salt. Process until smooth, adding more oil if needed, about 3 minutes. Transfer to a serving dish and sprinkle with smoked paprika.