Preheat oven to 350°F. Coat a 9- x 5- x 3-inch loaf pan with cooking spray.
Combine first 6 ingredients in a bowl; toss.
Add about 3 tablespoons milk to prepared pan. Arrange 1 layer of potatoes, shingle-style, over milk. Sprinkle with Parmesan. Repeat layers with remaining milk, potatoes, and Parmesan until pan is full. Top with Gruyère.
Cover pan with foil; bake 35 minutes. Uncover; bake until browned and bubbly and knife slides easily through potatoes, about 30 more minutes. Cool for 45 minutes before serving.
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