Heat oven to 400°F. Slice the top off a garlic head, drizzle with 1 tsp oil, and wrap in foil.
Roast until soft and golden, 35–40 minutes. Cool, then squeeze out cloves and measure about 2 tbsp.
Blend tahini and lemon juice in a food processor until creamy and light, about 30 seconds.
Add roasted garlic, salt, and cumin. Process to combine and perfume the base.
Add half the chickpeas. Blend, then drizzle in half the ice water and 1 tbsp olive oil.
Add remaining chickpeas with the rest of the water and oil. Process until very smooth, scraping as needed.
Taste and adjust salt or lemon. Swirl into a bowl, drizzle oil, and finish with paprika and parsley.