Preheat the oven to 400 degrees F.

Butter a 6-cup souffle or straight-sided baking dish with 11/2 tablespoons butter. Dust the interior of the dish with the Parmesan and knock out the excess.

In a large saucepan, melt the remaining butter over medium high heat. Stir in the flour and cook for 2 minutes, stirring constantly, until the butter and flour foam and froth. Remove the pan from the heat and beat in the hot milk, then simmer over medium heat and stir slowly until thick, about 1 to 2 minutes. Remove the pan from the heat and whisk in the seasonings, then the egg yolks, 1 by 1.

Whip the egg whites to stiff, shining peaks, then whisk 1/4 of them into the sauce to lighten it. Delicately fold the remaining egg whites into the sauce, alternating with the grated Swiss cheese.

Turn the souffle mixture into the prepared dish and set in the oven. Reduce the heat to 375 degrees F and bake until the souffle has puffed 1 or 2-inches above the rim and has browned on top, about 25 to 30 minutes. Serve immediately.