Place the potatoes and garlic in a large sauce pan. Cover with 1 to 2 inches cold water and season generously with salt. The water should taste like the sea. TASTE IT! If the water is under seasoned at this point it will be hard to have a well seasoned end product. Bring the pot of water to a boil and cook until the potatoes are fork-tender, about 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. Once the cream has come to a boil remove from the heat.
While the potatoes are still hot add 1/3 of the cream and butter and stir vigorously into the potatoes. Repeat this process 2 more times until all of the cream and butter has incorporated. 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.