Preheat oven to 325 degrees F.
Put the potatoes in a large saucepan with salted cold water to cover and bring to a boil over high heat. Cook until tender, about 10 minutes. Drain well, scatter onto a baking sheet and let cool for several minutes. Place in the oven to dry out, about 5 minutes. Smash the potatoes with a large fork or potato masher.
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 and cook quickly until pale gold. Add the cream, season, to taste, with salt and pepper, and bring to a boil. Reduce the heat to low and fold in 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.