The French-inspired cheese souffle is an elegant dish, simple to make, and best served immediately.
In a small bowl, mix together flour and 3 T. milk until smooth. Pour remaining milk into saucepan over low heat. Add butter and melt. Whisk in flour mixture and cook, stirring constantly, until thickened.
Remove from heat and stir in cheddar cheese, 1/4 tsp. salt and cayenne pepper. Transfer to a large bowl and let cool.
Preheat oven to 400 F.
Whisk egg yolks into cooled cheese mixture until well combined.
In a large glass bowl, whip all four egg whites until foamy and continue beating until stiff peaks form. Gently fold egg whites into mixture with a rubber spatula just until combined. Transfer mixture to a greased 1 1/2 quart souffle dish.
Place dish in oven and immediately reduce oven temperature to 375 F. Bake 30-45 minutes, or until souffle is puffed and golden and center moves only slightly when dish is shaken gently. (do not open oven door during first 20 minutes) Serve immediately.