Adjust oven rack to middle position and preheat oven to 400 degrees F. Grease a 2-quart baking dish with butter. Combine cheeses in a large bowl. Transfer 1/3 of cheese mixture to a separate bowl and set aside. Add cream, thyme, and garlic to cheese mixture. Season generously with salt and pepper. Add potato slices and toss with hands until every slice is coated with cream mixture, making sure to separate any slices that are sticking together to get the cream mixture in between them.
