Heat the oven and prep the dish: Preheat the oven to 375°F. Rub a 9x13 baking dish with 1 tablespoon of the butter, getting up the sides.

Slice the potatoes: Peel the potatoes and slice them 1/8 inch thick, ideally on a mandoline. Drop the slices into a bowl of cold water as you go so they don't brown, then drain and pat them dry right before layering.

Start the sauce: Melt the remaining 4 tablespoons of butter in a saucepan over medium heat. Add the onion and cook for 4-5 minutes until translucent, then stir in the garlic and cook 30 seconds more.

Cook the roux and add the dairy: Sprinkle in the flour and whisk constantly for 1-2 minutes. Slowly whisk in the milk, then the cream, and simmer for 3-4 minutes until the sauce thickens enough to coat the back of a spoon. Stir in the salt, pepper, thyme, and nutmeg.

Layer the pan: Shingle half the potato slices into the dish in overlapping rows. Pour half the sauce over them and spread it to the edges. Repeat with the remaining potatoes and sauce, pressing the top layer down gently so the slices sit in the sauce.

Bake covered: Cover the dish tightly with foil and bake for 50 minutes. The foil traps steam, which is what cooks the potatoes through before the top ever browns.

Bake uncovered: Remove the foil and bake another 25-30 minutes, until the top is golden brown, the sauce is bubbling at the edges, and a knife slides into the center with no resistance at all.

Rest and garnish: Let the dish rest for 15 minutes so the sauce sets up, then scatter the parsley over the top and serve.