Bring a small pot of water to a boil, then add the garlic and boil for 2 minutes; drain and peel.

Return the pot to the stove, turn the heat to medium, and add 4 tablespoons of the butter and the garlic and cook until soft, 15–20 minutes.

Stir in the flour and cook for 2 minutes, then add the milk and cook until thick and bubbling, 3–4 minutes more.

Using an immersion or regular blender, purée.

To a large pot, add the potatoes and enough generously salted water to cover by 1 inch. Bring to a boil, then turn down the heat to maintain a strong simmer and cook until tender, about 15 minutes.

Drain, then pass through a potato ricer back into the pot (alternatively, use a potato masher to finely mash).

Turn the heat to medium-low and gently stir in the remaining butter, reserved sauce, the cream, parsley, salt, and white pepper and cook until heated through, about 2 minutes more.