Step 1Heat the oven to 375 degrees. Use 1 tablespoon of the butter to grease a 6-cup souffle dish. Sprinkle with 1 tablespoon of the flour and turn the dish to coat the interior very lightly, then shake out the excess.
Step 2Bring the milk just to a simmer in a small saucepan. Melt the remaining butter in a medium saucepan over medium heat. Whisk in the remaining flour and cook, whisking constantly, until the mixture is smooth and bubbly, about 3 minutes. Whisk in the hot milk and continue whisking until the mixture thickens and is smooth, about 7 minutes. Season with salt, pepper and cayenne. Remove from the heat, transfer to a mixing bowl and cool slightly.
Step 3Add the egg yolks and cheese to the white sauce and mix very well. Beat the egg whites until stiff peaks form. Gently fold one-third into the cheese mixture so that the whites are evenly incorporated. Repeat with another third and finally with the last of the egg whites. Scrape into the prepared dish. Bake 25 minutes. If the top is not nicely browned and the souffle does not seem puffed and set in the center, bake 5 minutes longer.