Bring a large pot of water to a boil; add the basil and cook uncovered until bright green, about 20 seconds. Immediately plunge basil in ice water until cold. Squeeze basil to remove excess moisture and pat dry with a paper towel.
Put basil, garlic, lemon juice, 1 tablespoon olive oil, garbanzo beans, and white beans, salt, and black pepper, respectively, in a blender. Cover and blend until almost smooth; add remaining 2 tablespoons olive oil and puree until smooth.
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