Soak the beans: Place chickpeas and navy beans in a bowl, cover with several inches of water, and soak overnight. The next day, agitate beans in water, drain, and rinse.
Cook the beans (stovetop): Place beans in a heavy-bottomed pot, cover with water by an inch or two, bring to a boil, then reduce to low and simmer until tender, 1–2 hours. Add more water as needed. OR (Instant Pot/pressure cooker): Cook beans, covered with water by an inch or two, on high pressure for 15 minutes. Let pressure release naturally or quick release. Ensure beans are tender. Drain, reserving 1 cup cooking water.
Blend (immersion blender): Combine cooked beans, 1 cup reserved cooking water, lemon juice, and salt in a bowl. Blend 3–5 minutes until smooth. Add tahini and blend until creamy. OR (food processor): Place beans, cooking water, lemon juice, and salt in the processor. Blend until smooth. Add tahini and continue until fully combined. Note: The hummus may seem thin—it will thicken as it cools.
Serve: Spoon hummus into a bowl. Create a shallow well in the center and drizzle with olive oil. Sprinkle with paprika and serve warm or at room temperature with pita, pickles, or fresh vegetables.