Move oven rack to center and preheat oven to 350 degrees F. Grease 8x8-inch baking dish with butter.

In small saucepan, place 4 Tbsp. butter over medium-low heat. When melted and no longer bubbling, sprinkle in flour and whisk into a thick paste. Reduce heat as needed to prevent burning.

While whisking, gradually pour in milk. Stir in salt and pepper. Bring to a gentle simmer and continue whisking until smooth and thickened. Turn off heat and stir in 1 cup parmesan until melted.

Arrange half sliced potatoes in prepared baking dish and cover with half cheese sauce. Add remaining potato slices and sauce. Top with remaining ½ cup parmesan.

Bake until potatoes are fork-tender and top is crisp and golden, about 1 hour. Check halfway through and cover dish with aluminum foil if the top is darkening too fast. Let potatoes cool 5 to 10 minutes before sprinkling with thyme leaves and serving.