Place the potatoes and garlic in a large saucepan. Cover with 1 to 2 inches cold water and season generously with salt; the water should taste like the sea. Bring the pot of water to a boil and cook until the potatoes are fork-tender, 20 to 25 minutes.
Drain the potatoes and garlic well and pass through a food mill or ricer. DO NOT use a food processor or blender; it will result in a very sticky and rubbery end product.
While passing the potatoes, bring the heavy cream to a boil in a small saucepan and remove from the heat.
While the potatoes are still hot, add one-third of the cream and the butter and stir vigorously into the potatoes. Repeat this process with the remaining cream until you achieve a velvety and smooth consistency. Taste the potatoes for seasoning and add salt if needed. Serve immediately or cover with foil and keep warm in an oven on low heat.
Recipe courtesy of Anne Burrell