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.
Make it ahead: Assemble the dish, including the parmesan, and refrigerate for up to 3 days. Bake before serving.
Photograph by Johnny Miller
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