Preheat the oven to 375 degrees F.
In a small sauce pan or skillet, brown the onion in butter over medium heat and pour in the milk. Bring to a simmer and turn off heat to let it infuse.
With a pastry brush, coat the inside of a souffle dish with melted butter, bread crumbs and about 1 tablespoon of the cheese and place in the refrigerator.
Sweat the shallots in butter over medium heat, then add the vermouth and simmer for a few minutes.
Beat the whites with the cream of tartar until soft peaks form.
In a large sauce pan, make a roux by melting butter over medium-low heat and adding the flour, whisking constantly until bubbles form.
Remove the onion from the milk, and slowly whisk the liquid into the roux.
Add the shallots followed by the nutmeg and whisk over low heat until it thickens.
Beat the egg yolks and incorporate them into the roux along with cayenne.
Pour in the cheese and stir, then fold in the egg whites gently until mixture is uniform.
Pour the mixture into the souffle dish and bake for 25-30 minutes until brown on top and well raised above the dish. Refrain from opening the oven to check until 20 minutes have passed.
Serve immediately before it collapses!