Preheat the oven to 375 degrees F.
Put the cream, half-and-half, horseradish, nutmeg, garlic and onion in a medium saucepan and slowly bring the mixture to a simmer. Be sure to stir on occasion to prevent scorching. Season with salt and pepper.
In a 9-by-13-inch baking dish, spoon a thin layer of the cream and onion mixture onto the bottom. Layer the potatoes, followed by a sprinkle of cheese. Season lightly with salt and pepper. Repeat this process until the dish is filled and the gratin is moist. Combine the breadcrumbs and thyme and sprinkle on top.
Bake until the potatoes are tender and the gratin is caramelized on top and bubbly on the edges, 45 minutes to 1 hour. Allow to cool slightly before serving.