Melt 4 tablespoons of the butter in a large, oven-safe high-sided skillet over medium-high heat. When the foam subsides, add the flour and cook, stirring constantly, until it has the consistency of wet sand, about 3 minutes. Remove from the heat and whisk in the milk, little by little.
Put the saucepan over high heat and bring to a boil, whisking constantly. Lower the heat and whisk in 2 cups of the Cheddar, 2 cups of the Gruyere, the garlic, pepper and salt. Whisk until the cheese is melted, then stir in the nutmeg. Add the sliced potatoes to the pan. Scatter the remaining 2 tablespoons butter and the remaining 1 cup Cheddar and 1 cup Gruyere over the top.
Bake in the oven for 45 minutes, then increase the oven temperature to 400 degrees F., and bake until the potatoes are fork-tender and the top is bubbly and golden brown, about 15 minutes more. (Cover the dish with foil if the top becomes too dark before the potatoes are tender.) Scatter the chopped parsley over the top, and serve.