In a small bowl, whisk together the melted butter, heavy cream, and minced garlic until well combined.
Set your oven to 350°F. While it's warming up, you have time to slice the potatoes and grate the cheese.
Cut the potatoes into thin slices, about 1/8 inch thick. A mandoline slicer is a handy tool for this, but a sharp knife will do just fine.
In a greased 9x13 inch baking dish, arrange a third of the potato slices. Drizzle with a third of the creamy mixture, and season with a third of the salt, pepper, and thyme. Sprinkle with 3/4 cup of the grated cheese.
Create two more layers following the same pattern as the first, but hold off on adding cheese to the top layer—we'll get to that later.
Cover the dish with foil or a lid and bake for about 1 hour and 15 minutes. Check if the potatoes are tender by inserting a knife into the center. If they need more time, give them up to 15 additional minutes.
Once the potatoes are tender, remove the cover and sprinkle the remaining cheese on top. Bake uncovered for another 10 to 15 minutes, or until the cheese is golden and bubbly.
Let the dish stand for about 5 minutes before serving.