Place the potatoes, garlic, and 1 tablespoon of salt in a large pot with enough water to cover the potatoes. Bring to a boil over high heat, reduce to a simmer, and cook for 20 to 25 minutes, until very tender.
Drain the potatoes and garlic and process them together through a food mill fitted with the coarsest blade set over a bowl. While the potatoes are still hot, stir in the goat cheese, butter, sour cream, half-and-half, 4 teaspoons salt, and 2 teaspoons pepper, until smooth.
Pour the mixture into a 9-by-12-by-2-inch oval baking dish, smoothing the top. Sprinkle the Parmesan on top and bake for 30 to 40 minutes, until lightly browned. Serve hot.