Preheat the oven to 375°F with a rack positioned in the lower third of the oven, and the rack above it high enough to allow the soufflé to rise a few inches above the top of the pan. Using 1 tablespoon of the butter, grease 4 2-cup soufflé dishes. Place about 1 ½ teaspoons of the Parmesan in each dish, and shake the dish so that the cheese coats the bottom and sides.
In a large saucepan, melt the remaining 3 tablespoons butter over medium heat. Whisk in the flour and keep whisking for about 2 minutes until the mixtures gets a bit foamy. Whisk in the cayenne, remove the pan from the heat, whisk in the hot milk, then return the pan to the heat and simmer, whisking all the while. Add the Gruyere and the remaining 2 tablespoons Parmesan and whisk until the cheese melts and the mixture thickens.
Remove the pan from the heat and whisk in the mustard, salt and pepper. Whisk in the egg yolks one at a time, whisking quickly until they are completely incorporated.
In a large metal bowl, use a large whisk or an electric mixer to beat the egg whites until they started to become foamy, then add the cream of tartar and continue beating until the whites form stiff peaks with a little droop at the very tip. Transfer about ¼ of the egg whites to the yolk mixture, stir until just blended, then dump half of the rest of the beaten whites into the yolk mixture use a flexible spatula to gently fold in the whites. Repeat with the rest of the whites, folding just until barely blended, with a few streaks of white remaining.
Turn the mixture into the prepared dishes, smooth the tops, and run your thumb around the inside rims to remove any bits of Parmesan and also to allow the soufflés to rise to their fullest height. Bake for 20 to 25, until the tops have risen about 1 to 2 inches above the rim and barely jiggle a bit when you lightly shake the dishes. Serve immediately.
Notes
The right whipped consistency and careful folding are key to the perfect soufflé.