Preheat oven to 400°F (200°C). Grease a baking dish.
In a large saucepan, melt the butter with garlic until fragrant, about 1 minute. Stir in flour and cook for 1–2 minutes to make a light roux.
Slowly whisk in the cream and cook until slightly thickened, about 1–2 minutes. Add Parmesan, thyme, salt, and pepper, then whisk until smooth. You can adjust the thickness by adding a little milk if needed.
Arrange the sliced potatoes in the baking dish. Pour the creamy sauce evenly over the top and sprinkle extra Parmesan if you like.
Cover with foil and bake for 30 minutes. Remove foil and bake another 30 minutes until the potatoes are soft and the top is golden.
Let it rest for 10 minutes before serving so everything sets nicely.