Preheat the oven to 325°F (160°C). Peel the outside papery skin off the garlic heads. Create 3packets of garlic by wrapping 5 heads together in aluminum foil.
Bake the garlic until the cloves are soft, usually about 1 hour.
Extract the purée from the cloves with a food mill, or by pushing the garlic flesh through a drum sieve with a plastic pastry scraper or a strainer with the back of a ladle.
To store the purée in the refrigerator, place in mason jars or narrow containers, smooth the top with the back of a spoon, and dribble over the olive oil. Seal the jars or cover with plastic wrap. The purée darkens when exposed to air.