First preheat oven to 375ºF (190ºC). In a small dish, press together softened butter and garlic and rub across the bottom of a 9 x 13-inch (28 x 33 cm) baking dish.
Using a sharp knife or mandolin, cut potatoes into very thin, 1/8-inch (3 mm) slices. Layer half the potatoes, overlapping, in the prepared pan. Season generously with salt, pepper and half the thyme leaves.
Next, make a second layer of potatoes and pour cream over the top, distributing evenly. Season once again with salt, pepper and more fresh thyme and sprinkle the grated cheeses across the top.
Cover with foil and bake for 30 minutes. Remove foil and bake for 20-30 more until the potatoes pierce easily with a fork and everything is golden brown and bubbling. Let rest for at least 15 minutes before serving to allow the sauce to thicken. Enjoy!