Preheat oven to 400°F. Butter a 2-quart casserole pan with butter.
In a large bowl mix both the cheeses together than remove about 1/3 of it and set aside. Mix the half & half, garlic, thyme, a generous teaspoon salt and 1/4 teaspoon black pepper into the cheese.
Add the sliced potatoes and toss using your hands making sure every slice is coated. Makes small stacks out of the potatoes and stand them in the pan starting at one edge and working around the perimeter then into the center last.
Pour the remaining half & half left in the bowl over the potatoes. Season the top with more salt and pepper.
Cover tightly with aluminum foil and bake 20 minutes. Remove the foil and sprinkle the top with the cheese you set aside. Bake 40 more minutes until the top is golden and the potatoes are fork tender.
Remove from oven and let set 5 minutes before serving.