Preheat oven to 400°F. Grease a 2-quart baking dish and set aside.
Melt the butter in a large skillet over medium heat. Whisk in the flour and garlic; cook for 1 minute. Gradually whisk in the milk and cream. Cook, whisking, until the sauce thickens, about 2 minutes.
Add the thyme, salt, pepper, nutmeg, and half of each cheese. Whisk for about 1 minute until the cheese is fully melted. Taste and adjust seasoning as needed.
Arrange half of the potatoes in the prepared baking dish. Season lightly with salt. Pour half the sauce over the top. Layer the remaining potatoes on top, season again, and pour the rest of the sauce over everything. Sprinkle with the remaining cheese.
Cover and bake for 50 to 60 minutes, until the potatoes are just about tender. Remove the cover and bake for another 15 to 20 minutes until the top is golden and bubbling.
Let the dish rest for 10 to 15 minutes before serving.