With the rack in the middle position, preheat the oven to 165 °C (325 °F). Slice the top off the heads of garlic. Place in the centre of a sheet of aluminum foil. Drizzle with olive oil and close to seal the foil.
Bake for about 1 hour and 30 minutes, along with the whole turkey, at its lowest heat setting (see note). Press out the caramelized garlic pulp. Set aside.
Meanwhile, in a large pot of salted water, cook the potatoes until very tender. Drain. Using a masher, coarsely crush the potatoes with the butter and garlic purée. With an electric mixer, purée the potatoes until smooth with the cream, milk, and thyme. Add milk, if needed. Season with salt and pepper.
Count about one large russet potato per person. If you are not roasting a turkey, you can roast the garlic at 180 °C (350 °F) for about 45 minutes.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.