Preheat the oven to 350 degrees F.

Peel the outermost layers of skin off the heads of garlic. Cut off the top ⅓ of the heads to open the cloves.

Heat olive oil in a large oven-safe saute pan over medium heat. Add garlic, cut sides up, and saute for about 10 minutes. Season with salt and pepper.

Transfer pan to the oven and roast for 15 minutes. Alternatively, drizzle cloves with olive oil, and sprinkle with salt and pepper. Wrap in aluminum foil and cook for 30-45 minutes, or until soft (almost mushy) and golden.

Remove from heat and let cool. Pop garlic cloves from their skins and place cloves in a food processor, along with ¼ cup olive oil. Puree until smooth; you should have a paste-like consistency.

Peel and cube the potatoes. Put the potatoes in a large saucepan with salted cold water and place in the refrigerator overnight (or 30 minutes).

Add some more salt and then bring to a boil over high heat. Cook until tender, about 10 minutes. Drain well and return to pot.

Over very low heat, stir and mash the potatoes. Doing this over low heat will let the remaining water evaporate out of the potatoes, making for an even fluffier final product.

Meanwhile, heat 1 tablespoon of the butter in a large saucepan over medium heat until the butter stops foaming and turns a light brown.

Add the garlic paste and cook quickly. Add the cream, season to taste with salt and pepper, and bring to a boil.

Reduce the heat to low and fold cream mixture into potatoes with a wooden spoon or large whisk.

Add the remaining butter by tablespoons, stirring after each addition. Stir in the extra-virgin olive oil. Season with salt and pepper to taste, and serve.