How to Make It
Preheat oven to 375°. Sauté shallots in 3 Tbsp. melted butter in a saucepan over medium heat 2 minutes. Stir in cream and next 5 ingredients; cook 2 minutes. Remove from heat; cool 15 minutes.
Meanwhile, peel and thinly slice all potatoes. Combine sliced potatoes and milk in a large, microwave-safe bowl. Cover with plastic wrap, and microwave at HIGH 5 minutes. Uncover and gently stir mixture. Re-cover and microwave 5 more minutes. Drain mixture, discarding milk.
Layer one-third of Yukon gold potatoes in a well-greased (with butter) 9- x 13-inch baking dish; top with one-third of sweet potatoes. Spoon one-third of cream mixture over potatoes, and sprinkle with 1/2 cup Gruyère cheese. Repeat layers twice, and top with Parmesan cheese. Cut remaining 1 Tbsp. butter into small pieces, and dot over top. Cover with foil.
Bake at 375° for 30 minutes. Uncover; bake 20 minutes or until browned. Let stand 10 minutes.