Preheat the oven to 375°F with a rack in the center. Grease a 9×13-inch baking dish with 1 tablespoon butter and place it on a rimmed sheet pan.
Melt the remaining 3 tablespoons butter in a medium saucepan over medium heat. Cook the onion for 5 to 6 minutes until soft, then stir in the garlic for 30 seconds. Add the flour and whisk for 1 minute.
Pour in the milk gradually while whisking, then add the cream, salt, pepper, nutmeg, and thyme. Simmer gently for 4 to 5 minutes until the sauce lightly coats the back of a spoon.
Layer one-third of the potato slices in the baking dish in overlapping rows. Spoon over one-third of the warm sauce, reaching the corners. Repeat twice with the remaining potatoes and sauce.
Cover tightly with foil and bake for 50 minutes, until a knife meets some resistance but passes through every layer.
Remove the foil and bake for 25 to 30 minutes more, until the center bubbles and the top is golden. Rest for 15 minutes, then scatter chives over the top before serving.