Drain the chickpeas and transfer to a large pot and fill with fresh tap water. Cook until soft, about 2 hours. (Conversely, save time by using canned chickpeas, about 3 cans for the equivalent).
Meanwhile, make the pesto by mixing the basil with garlic paste and olive oil till creamy.
When cooked, save the cooking water and transfer most of the chickpeas to the bowl of a processor and cool a bit. Add the tahini, pesto and lemon juice and process, tasting to adjust some ingredients to your taste.
When it has reached the right texture and the taste that you like, transfer to a serving plate and garnish with the pistachios and some fresh basil leaves or extra chickpeas. Serve with pita bread or chips.