Heat oven to 375° F. Grease one 16-ounce or two 8-ounce ramekins with 1 tablespoon of butter. Coat with the Parmesan, then tap out the excess. Set aside.
In a small saucepan, over medium heat, melt the remaining butter. Stir in the flour and cook 1 minute. Whisk in the milk and cook, stirring constantly, until the sauce boils, 1 minute. Remove from heat and stir in the cheese until melted. Blend in the cayenne and nutmeg. Whisk in the yolks one at a time. Set aside. (The recipe can be made to this point up to 1 day ahead. Cover with plastic wrap and refrigerate.)
In a clean bowl, beat the egg whites with the salt until stiff (but not dry) peaks form. Stir 1/4 of the egg whites into the cheese sauce to loosen it. Gently fold in the remaining egg whites. Spoon into the ramekins. Bake until puffed and browned, 40 minutes for a 16-ounce soufflé, 20 minutes for two smaller ones. Serve immediately.