Prepare the potatoes. Preheat the oven to 400°F. Using a mandoline, or a sharp knife, thinly slice the potatoes 1/16-thick. Set aside. Finely dice the onion and mince the garlic. Set aside.

In a large skillet over medium heat, melt 1 tablespoon of the butter. Add the onions, thyme, and a pinch of salt, and cook for about 3 minutes, or until translucent. Add the garlic and cook for an additional 30 seconds. Add in remaining 4 tablespoons of butter. Once melted, whisk in flour until completely smooth. Allow to cook for 30 seconds to a minute to toast out the raw flour flavor. This creates a roux.

Slowly pour about 1/4 cup of the the milk into the roux, whisking until smooth. Once smooth, slowly pour in remaining milk, salt, and pepper. Cook for 3-5 minutes until a creamy sauce forms, whisking continually. This creates a béchamel.

Slowly sprinkle in the cheese, whisking after each addition until smooth. Cook a minute more. This creates an unbreakable cheese sauce. Remove from heat. Taste, adding more salt if necessary. Note: This sauce will be on the salty side to carry the weight for the potatoes.

In a 9″ x 11.5″ enamelware pan (or something similar), add enough sauce to coat the bottom of the pan. Begin adding potatoes like spilled dominos, overlapping about 1-inch (see image above), until you have a solid layer of potatoes. Liberally cover with sauce, then add potatoes. Repeat until all potatoes are used, ending with a layer of sauce. Tightly cover with foil and bake for 30 minutes.

Prepare the gratin. After 30 minutes, remove from oven. Discard foil and top with the gratin. Bake for 20-30 minutes more. Sprinkle with additional thyme and serve warm.