Direction :

1. Adjust the oven rack to the middle position and heat the oven to 400ºF.
2. Combine the cheeses in your largest bowl, see notes above. Transfer ⅓ of the cheese mixture (roughly 2/3 cup) to a separate bowl and set aside. Add the cream, stock, garlic, and thyme to the large bowl. Season generously with salt and pepper — I season with 1 tablespoon kosher salt (Diamond Crystal brand), and I do not find it to be too salty but use less if you are worried. Honestly, I think it could use even more salt — it’s a lot of potatoes.
3. Add potato slices and toss with your hands until every slice is coated with the cream mixture, making sure to separate any slices that are sticking together to get the cream mixture in between them.
4. Grease a 9×13-inch baking dish with the softened butter. Pick up a handful of potatoes, then transfer them to the baking dish with their edges aligned vertically. Continue placing potatoes in the dish, until all the potatoes have been added. The potatoes should be tightly packed. If necessary, slice an additional potato, coat with the cream mixture, and add to the baking dish. Pour the excess cream/cheese mixture evenly over the potatoes.
5. Cover the dish tightly with foil and transfer it to the oven. Bake for 30 minutes. Remove foil and continue baking until the top is pale golden brown, about 30 minutes longer. Carefully remove from oven, sprinkle with remaining cheese, and return to oven. Bake until deep golden brown and crisp on top, about 30 minutes longer.
6. Remove from oven, let rest for a few minutes, and serve.