Slice the root end off the entire head of garlic and turn it upside down, wrapping it in aluminum foil and molding the foil so it supports the garlic to allow the cut end to stand upright in the oven. Pour 1 tablespoon of the olive oil on the garlic (reserving the other tablespoon) so it slips between the skin and the cloves and wrap with the foil so it is enclosed. Roast for about 1 hour and set aside until it is cool enough to handle.
Bring a large pot of water to boiling for the pasta. Salt the water and boil until al dente. Drain and set aside.
Heat the milk in a small saucepot and keep warm. Squeeze the garlic cloves into a small bowl and mash them. Add a small amount of the warm milk to this bowl and whisk until smooth.
In a separate large saute pan, heat the remaining tablespoon of olive oil over medium high heat and saute the shallot until translucent. Deglaze the pan with the white wine and allow most of the wine to evaporate, then reduce heat to low, and add the garlic mixture. Whisk the goat cheese and Parmesan into the remaining hot milk, and add this to the pan with the garlic and wine sauce and season, to taste, with salt and pepper. Fold the drained pasta into the pan of sauce, transfer to serving dish and garnish with parsley sprigs.