Use a mandoline to thinly slice potatoes to 1/8 inch thick. Put into large bowl.
Add salt, black pepper to bowl and toss to coat as evenly as possible. Then add flour, thyme, garlic powder to the potatoes and toss again to distribute. Add 1/2 of cheese to potatoes and toss.
Butter a 7x10 baking dish and put half of potatoes into the dish, laying them flat. Add a little bit more cheese over the top of them. Then place remaining potatoes on top of the others, in a flat and organized manner. Sprinkle with remaining cheese.
Pour half and half over the potatoes, distributing evenly. Cover the top of the pan with aluminum foil and secure it tightly.
Bake for 30 minutes covered, then remove foil and increase temperature to 385 degrees F. Bake for 20-30 more minutes, until potatoes are cooked through, and can be pierced easily with a fork.