1. Preheat the oven to 400°F. Lightly grease a medium baking dish.

2. Slice the potatoes very thin, about 1/16 inch thick, using a sharp knife or mandolin.

3. In a large pot over medium heat, melt the butter. Add the garlic and cook until fragrant, about 30 seconds.

4. Stir in the flour and cook for 1 to 2 minutes, stirring constantly to form a smooth paste.

5. Gradually whisk in the milk and continue stirring until the sauce thickens, about 5 minutes.

6. Stir in the Parmesan cheese, thyme, salt, and pepper until smooth. Remove from heat and let cool slightly.

7. Place the sliced potatoes in a large bowl. Pour the sauce over them and gently toss to coat evenly.

8. Arrange the coated potato slices upright in the prepared baking dish. Pour any remaining sauce over the top. Sprinkle additional Parmesan if desired.

9. Cover loosely with aluminum foil and bake for 30 minutes. Remove the foil and bake for another 30 minutes, or until the potatoes are tender and the top is golden brown.

10. Let rest for 10 minutes before serving.