Butter a 6-inch diameter x 3 1/2 inches deep soufflé dish. Cut a 6-inch-wide strip of parchment paper, butter it, wrap it around the soufflé dish and tie it tight with a string.
Separate the eggs and yolks into two bowls, a small one for the yolks, a medium-sized one for the whites. Set aside.
Melt the butter in a medium-sized pot over medium heat. Stir in the flour and cook for 2 minutes.
Whisk in the milk until no lumps remain, turn the heat to medium low and cook until the mixture just comes to a slow boil.
Add in the cheese, stirring until it’s thoroughly melted. Beat the yolks with a fork and add them to the mixture, stirring constantly. Add the Dijon mustard, cayenne pepper, and salt, whisk it all together, and remove from heat. The mixture will be the consistency of a thick custard. Allow it to cool to room temperature, whisking occasionally to help it cool. While it’s cooling, preheat the oven to 375F.
With a clean whisk, beat the egg whites to stiff peaks. Add a couple of tablespoons to the cooled sauce and stir to loosen it up. Fold in the remaining egg whites with a spatula until no streaks remain.
Pour the mixture into the prepared pan. Bake for 35 to 40 minutes, until the soufflé has puffed up above the rim and the top is browned. Turn the oven light on so you can see and be sure to arrange the soufflé dish with the little window in the collar towards you.
Remove the soufflé from the oven, snip the string, remove the collar and bring the soufflé to the table, slowly, calmly. Serve with green salad and sauteed potatoes. Bacon and onion in the potatoes would not be overdoing it.