Generously butter a 2-quart soufflé dish or six 1- to 1 1/4-cup soufflé dishes; if using small ones, set them about 2 inches apart in a 10- by 15-inch baking pan.
In a 2- to 3-quart pan over medium heat, melt 1/4 cup butter. Add flour and stir until mixture is smooth and bubbling. Stir in milk, cayenne, and salt, and continue stirring until sauce boils and thickens, 3 to 4 minutes. Remove from heat.
Add cheese and stir until melted. Add egg yolks and stir until the mixture is blended and smooth.
In a bowl, with a mixer on high speed, beat egg whites (use whisk attachment if available) with cream of tartar until short, stiff, moist peaks form. With a flexible spatula, fold a third of the cheese sauce into whites until well blended. Add remaining sauce and gently fold in just until blended.
Scrape the batter into the prepared soufflé dish (or dishes). If the dish is more than 3/4 full, use foil collar (see "Crowning Glory," below). If desired, draw a circle on the surface of the soufflé batter with the tip of a knife, about 1 inch in from rim, to help an attractive crown form during baking.
Bake in a 375° regular or convection oven until top is golden to deep brown and cracks look fairly dry, 25 to 30 minutes for large soufflé, 15 to 20 minutes for small ones. Serve immediately, scooping portions from single soufflé with a large spoon.
Soufflés look most impressive when they rise dramatically over the rim of the dish. To create a beautiful crown on your soufflé, fill the dish about 3/4 full. If it's less full, the soufflé may not rise over the rim. If it's more full, the soufflé may spill over unless you wrap the dish with a foil collar. Here's how to make one.
Cut a 15-inch-wide sheet of foil 4 inches longer than circumference of dish; fold lengthwise in thirds. Coat one side of the foil strip generously with melted butter, using a pastry brush. Wrap the foil around outside of dish so that at least 2 inches of foil extend above the rim. Fold the ends of the buttered foil strip over several times until snug against dish.