Place chickpeas and 1/2 teaspoon baking soda in a medium bowl and add cold water to cover by 2 inches. Cover and let sit, at room temperature overnight, until chickpeas have doubled in size. Drain and rinse.
In a large saucepan, combine the soaked chickpeas and remaining 1/2 teaspoon baking soda and add cold water to cover by at least 2 inches. Bring to a boil, skimming if needed. Reduce the heat to medium-low, partially cover, and simmer until chickpeas are tender and squish easily between your fingers, about 45–60 minutes. Drain and set aside.
While the chickpeas are cooking, place the garlic, 2 tablespoons + 2 teaspoons of the lemon juice, and tahini in a blender or food processor and pulse until smooth. With the motor running, Add the ice water, 1 tablespoon at a time (it may seize up at first) until mixture is very smooth, pale, and thick.
Add the drained chickpeas and cumin and process, scraping down the sides as needed, until very smooth, about 4 minutes. Thin with water if a looser consistency is needed. Taste and season with lemon juice, and cumin, as desired.