Preheat oven to 250 Degrees. Cut off top of garlic head so you can just see tops of cloves peeking through. Discard top, then sit garlic on a piece of aluminium foil and seal ends tightly, while leaving parcel slightly baggy. Place on a small foil pan (or similar) and bake for 45 minutes. Let cool in foil wrapping.
Drain and rinse chickpeas (if using canned or jarred), then tip into a food processor. Add lemon zest and juice; squeeze in soft flesh from caramelized garlic. Spoon in tahini and 1/4 cup oil, then blitz to a smooth puree. Tip in up to 1/4 cup cold water to get the right consistency, blitzing as you go, then add 1 tsp. salt and pepper. Taste and season lightly with more salt if needed. Decant into a bowl. Drizzle with more oil, if desired, and serve.