Soak the chickpeas overnight in a large bowl of water with 1/2 teaspoon of baking soda. They will roughly double in size.
Drain and rinse. Put them in a pot with fresh water to cover by 2 inches and the remaining 1/2 teaspoon of baking soda. Bring to a boil, skim off any foam, and simmer for 45–60 minutes, until they are very soft and crush easily between your fingers.
Drain the chickpeas (save some cooking liquid) and let them cool slightly.
In a food processor, blend the lemon juice, garlic and salt; let it sit for a few minutes to mellow the garlic. Add the tahini and blend; it will thicken. With the motor running, add ice water a tablespoon at a time until pale and creamy.
Add the warm chickpeas and cumin and process for 2–3 minutes, scraping the sides, until very smooth. Thin with more ice water or cooking liquid if needed. Taste and adjust lemon and salt.
Spread in a shallow bowl, drizzle with olive oil, and dust with paprika.