Preheat the oven to 400°F and grease a ceramic baking dish.
Peel and thinly slice the potatoes using a mandoline or sharp knife.
Melt the butter in a large pot over medium heat, then add the garlic and cook until fragrant.
Stir in the flour and cook briefly to form a roux.
Gradually whisk in the cream and cook until slightly thickened.
Stir in the Parmesan cheese, thyme, salt, and pepper until smooth.
Add the sliced potatoes and gently toss to coat evenly in the sauce.
Arrange the potatoes upright in the baking dish and pour any remaining sauce over the top.
Sprinkle additional Parmesan cheese on top.
Cover with foil and bake for 30 minutes, then uncover and bake another 30 minutes until golden and bubbling.
Let rest for 10 minutes before serving.