Use a 6-8 cup souffle dish or 4 individual 10 ounce souffle dishes.
Pull a sheet of aluminum foil slightly more then 3 times longer then the diameter of the dish and fold it lengthwise over itself with the shiny side showing. The foil strip should be wide enough to cover the outside of the dish and rise at least 3 inches above the rim.
Rub the strip of foil and the inside of the dish with softened butter. Wrap the foil around the dish and attach it by pinching together at the top so it stays in place (you can also use a paper clip).
Evenly sprinkle the Parmigiano-Reggiano all around the dish and the foil until they are covered with a layer of cheese. Do NOT touch the inside after this point. Put dish in refrigerator.
Make the Mornay Sauce: Melt butter in a small, heavy-bottomed saucepan and stir in the flour with a whisk until smooth. Gradually pour in milk while whisking and bring to a simmer over high heat, while continuing to whisk. Boil for a couple of minutes until sauce thickens a bit and mixture is smooth. Remove from heat, stir in Parmigiano-Reggiano, and season with salt, pepper and nutmeg. Whisk in egg yolks one at a time. Reserve up to 2 days, covered.
Preheat oven to 350°F if you are using a 6 or 8 cup souffle dish or to 375°F if you are using individual souffle dishes.
Beating and Folding: Put egg whites into a very clean bowl of standing mixer fitted with whisk. Turn on low to break up the whites. Add a pinch of salt and a small pinch of cream of tartar. Gradually increase speed to high. Keep a sharp eye on the whites, it only takes about 4 minutes to get to stiff peaks – that’s when they stick straight out when you hold the whisk or beater sideways, instead of softly flopping over. Take the bowl off the standing mixer and finish the soufflé by hand (or 6-8 minutes by hand).
Take out one-fourth of the beaten whites and stir into 1 cups of the cooled (but not cold) Mornay Sauce – this lightens up the Mornay and makes it easier to fold in the whites.
Pour the Mornay Sauce down the side of the bowl containing the remaining whites and sprinkle the 3/4 cup finely grated cheese over the top. Fold everything together using a rubber spatula, pressing the spatula down to the bottom of the bowl where most of the heavier sauce base will have settled and lift up the base, gently folding it over the whites. Continue cutting into the whites, but not pushing against them, to combine the mixture. Don’t overdo it; a few uncombined pieces of white are less of a problem than overworking the mixture.
Gently pour the mixture into the soufflé dishes – the mixture should come up somewhere between 3/4ths of the way up and the top. Slide the sheet pan of soufflés into the oven. Turn up the oven to 375°F or to 385°F if making individual souffles.
Bake a large souffle for 40 to 50 minutes or individual souffles for 15 to 20 minutes. Soufflés are done when risen about half its original height and when sheet pan jiggled back and forth the tops won’t rock – if the insides are underdone, the tops will rock slightly.
Side Note: If you rush the soufflé to the table and cut into it and see that it’s undercooked, don’t panic. Be as nonchalant as possible and just put soufflés back in the oven and cook it a few more minutes. An underdone soufflé won’t fall much once out of the oven, an overdone one will. .
Take the sheet pan with the soufflés out of the oven and immediately pull away the collar, and bring the souffle to the table. If you are serving individual soufflés, put each souffle on a plate and sit it before a guest. If you are serving one big soufflé, serve it at the table on heated plates. Make sure everyone gets some savory crust. The creamy center should function as a sauce for the rest.