Drain the beans (no need to rinse). If using chickpeas, peel each one individually and discard the skins.
Add the tahini to a food processor and pulse several times. Turn the machine on and slowly add 1/4 cup of ice water. If the tahini is clumping, add the additional 1/4 cup water 1-2 tablespoons at a time. Puree for 1-2 minutes, until the tahini is a whipped, creamy consistency. Scrape down the bowl.
Add the beans and garlic, then puree until smooth. Turn the machine back on and slowly add the olive oil, lemon juice and salt.
Taste, and adjust the seasoning if desired.
Recipe prep time reflects using white beans. Add 10 minutes if peeling chickpeas.