Preheat the oven to 350 degrees.
In a saucepan, melt the butter then stir in the flour. Add the milk, cayenne and Dijon mustard and continue to stir until thickened.
Add the cheese a little bit at a time and mix well. Remove from heat.
Separate the egg yolks and egg whites into two bowls.
Beat the egg yolks with a fork and then add the cheese sauce to the eggs yolks. Stir well and allow the mixture to cool.
Using a standing or hand mixer, beat the egg whites until stiff peaks form. This usually takes 2-3 minutes.
Carefully pour the cheese and egg yolk mixture into the egg whites and gently combine.
Pour into a souffle dish or large ramekin and bake on the bottom rack of the oven at 350 degrees for 45 minutes.
Allow the Cheese Soufflé to cool before serving.
