Bring a small pot of water to a boil, then add the garlic and cook for 2 minutes; drain and peel.
In a medium pot set over medium heat, melt 4 tablespoons of the unsalted butter, then add the garlic and cook until soft, 15 to 20 minutes.
Stir in the flour and cook for 2 minutes, then add the whole milk and cook until thick and bubbling, 3 to 4 minutes.
Using an immersion or regular blender, purée.
To a large pot, add the russet potatoes, cut into 1 inch pieces, and enough generously salted water to cover by 1 inch. Boil until tender, about 15 minutes, then drain and pass through a potato ricer back into the pan (alternatively, use a potato masher to finely mash).
Turn the heat to medium-low and stir in the remaining butter, reserved sauce, the heavy cream, parsley, salt, and white pepper and cook until heated through, about 2 minutes more.