Add the tahini, cold water, olive oil, cumin, salt, garlic, and lemon juice to a food processor and blend until smooth. Add the chickpeas and blend for several minutes, until completely smooth. If the mixture is too thick, add 1-2 tablespoons of water to thin it out a little.
Refrigerate until ready to serve. Serve with fresh vegetables and pita bread on the side for dipping. For a prettier presentation, drizzle with olive oil and sprinkle with paprika before serving.