Preheat the oven to 375 degrees F. Place the potatoes, garlic and 1 tablespoon 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 on top of 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.
Photograph by Johnny Miller
Make it ahead: Assemble the dish, including the parmesan, and refrigerate for up to 3 days. Bake before serving.
Recipe from Make It Ahead: A Barefoot Contessa Cookbook Copyright (c) 2014 by Ina Garten. By arrangement with Clarkson Potter/Publishers, A Division of Random House LLC