Bring the cream, garlic, and thyme just to a boil in a small saucepan over medium heat, stirring frequently. Cook and stir for 1 minute. Remove from the heat. Gradually stir in the parmesan until melted. Season with salt and pepper to taste.
Place half the potatoes in a single layer, overlapping the edges, on a greased 15 x 10-inch baking pan. Season with salt and pepper. Pour half the parmesan sauce over the potatoes. Sprinkle with 3/4 cup each of cheddar and Grand Cru®. Repeat this step with the remaining potatoes, cheese sauce, and cheeses.
Bake, covered, for 20 minutes. Uncover and bake for another 20-25 minutes or until the cheese is bubbly and the potatoes are tender.