Whisk until the cheese is melted, then stir in the nutmeg. Lower the heat and whisk in 2 cups of the Cheddar, 2 cups of the Gruyere, the garlic, pepper and salt. Put the saucepan over high heat and bring to a boil, whisking constantly. Remove from the heat and whisk in the milk, little by little.
When the foam subsides, add the flour and cook, stirring constantly, until it has the consistency of wet sand, about 3 minutes. Melt 4 tablespoons of the butter in a large, oven-safe high-sided skillet over medium-high heat.
