Preheat the oven to 425°F Chill four 1/2-cup souffle dishes in the refrigerator.
Use one tablespoon of the butter to butter the bottom and sides of each souffle dish, paying special attention to the sides. Return to refrigerator.
Melt the remaining butter in a saucepan and add the flour, stirring with a wire whisk until well-blended. Cook until raw taste is gone, 2-3 minutes, but do not brown the flour. Add the milk, stirring rapidly with the whisk, then add the salt, pepper, nutmeg and cayenne. Bring to a boil and cook for 30 seconds, stirring constantly with the whisk.
Blend the cornstarch and water in a bowl or small jar. Add to the bubbling sauce. Stir and cook for about two minutes. Add the yolks, stirring vigorously. Cook, stirring, for about a minute.
Transfer the hot sauce to a large mixing bowl. Add the cubed cheese and stir well. Set aside.
Beat the egg whites to stiff peaks. Add half of the whites to the souffle base and mix thoroughly. Add the remaining whites, folding them in quickly but gently with a rubber spatula.
Divide the mixture evenly into the four souffle dishes. The mixture should fill the dish to about a quarter-inch from the top of the dish. With your thumb, create a channel around the edge of the dish to allow for expansion and formation of a nice crown. Sprinkle the top with the grated gruyere.
Place the dishes on a baking sheet on the bottom rack of the oven and bake for 12 to 15 minutes. Serve immediately.