Preheat the oven to 400°F. Line a 10-by-15-inch baking sheet with parchment or waxed paper. Put a few dabs of butter on the pan to help anchor the paper; then lightly butter and flour the paper, knocking off any excess flour.

Separate the yolks and the whites; lightly beat the yolks and set them aside. Heat the milk and make the roux: Melt the butter, add the flour, and, stirring constantly, cook for 1 to 2 minutes over medium heat until the roux is lightly colored. Whisk in the heated milk, and cook for another 3 minutes, stirring constantly; then remove from the heat and season with ½ teaspoon salt and the cayenne. Gradually whisk some of the hot mixture into the yolks to warm them; then return to the pan to finish combining.

In a large bowl, whisk or beat the egg whites with a pinch of salt until they form smooth, firm peaks. Stir about a quarter of the whites and half the grated cheese into the milk-egg yolk mixture; then gently fold in the rest of the whites. Pour the souffle mixture onto the baking sheet, spread it to fill all the comers, and sprinkle the rest of the cheese over the surface. Bake until the top is nicely browned and puffed, about 15 minutes.

Remove the souffle from the oven and let it cool. Carefully turn it out onto a counter by turning over the pan, and remove the paper. It is now ready to be filled and rolled.