Preheat the oven to 350˚ F. Remove outer papery skins from the garlic heads. Chop off the top quarter of garlic heads so that all of the cloves are exposed. Wrap the garlic in foil and roast until very tender, about 1 hour. Meanwhile, heat 2 tablespoons of olive oil and sliced garlic cloves in a small skillet over medium-low heat. Cook, stirring occasionally, until golden brown, about 15 minutes. Use a slotted spoon to transfer the garlic to a paper towel-lined plate and set aside; reserve oil. Once the roasted garlic is cool enough to handle (about 10 minutes), squeeze the cloves from their skins (you should have about ¼ cup).
In a small bowl, combine lemon juice and water. In a separate bowl, whisk together the tahini reserved garlic cooking oil. In the bowl of a food processor, process chickpeas, roasted garlic, minced garlic clove, salt and cayenne until the mixture is almost fully ground, about 15 seconds. Scrape down bowl. With the food processor running, add the lemon juice-water mixture through the feed tube in a steady stream. Scrape down the bowl and process for 1 minute. With the machine running, add the oil-tahini mixture through the feed tube in a steady stream. Scrape down the bowl and continue to process until the hummus is smooth and creamy.
Transfer hummus to a serving bowl, top with toasted garlic slices and minced fresh parsley. Cover with plastic wrap and let stand until flavors meld, at least 30 minutes. Drizzle with olive oil and serve.