Preheat the oven to 350°F. Wrap the prepared garlic heads tightly in aluminum foil and roast until the cloves are browned and very tender, about 1 hour.

Combine the olive oil and sliced garlic in an 8-inch skillet over medium-low heat. Cook, stirring occasionally, until the garlic slices are golden brown and crisp, about 15 minutes.

Transfer the toasted garlic slices to a paper towel–lined plate using a slotted spoon, leaving the infused oil in the skillet to cool. Once the roasted garlic heads are cool enough to handle, squeeze the softened cloves from their skins into a small bowl to form a paste.

Place the chickpeas, roasted garlic paste, tahini, lemon juice, salt, and the reserved garlic-infused oil in a food processor. Process until the mixture is completely smooth and creamy, about 2 minutes, adding water one tablespoon at a time if the consistency is too thick.

Transfer the hummus to a shallow serving bowl. Garnish with the toasted garlic slices, minced parsley, and a final drizzle of olive oil. Serve at room temperature with warm pita or fresh vegetables.