Prepare the Onions: Peel all the onions. Quarter 5 of them and place them in a pot with enough lightly salted water to cover.
Bring to a boil and cook until completely tender, about 15-20 minutes.
Drain the onions, reserving ⅓ cup / 80 ml (2.7 fl oz) of the cooking water.
Mince the cooked onions finely. Finely chop the remaining raw onion.
Make the Soufflé Base: In a medium, heavy-bottomed saucepan over medium heat, melt the 4 Tbs. of butter.
Add the finely chopped raw onion and sauté until softened and just beginning to turn golden.
Lower the heat, stir in the flour, and cook for 2 minutes, stirring constantly with a wooden spoon to create a roux. Slowly whisk in the reserved ⅓ cup of onion water and the heavy cream.
Continue stirring over low heat until the mixture is perfectly smooth and very thick.
Flavor the Base: Remove the saucepan from the heat.
Stir in the minced cooked onions, salt, white pepper, nutmeg, cayenne, and the 2 Tbs. of grated Parmesan cheese. Quickly whisk in the egg yolks one at a time until the mixture is smooth and glossy.
Fold in the Egg Whites: In a separate, spotlessly clean bowl, beat the egg whites and cream of tartar with an electric mixer on high speed until they form stiff, shiny peaks.
Stir about one-quarter of the beaten egg whites into the onion base to lighten it.
Then, gently fold in the remaining whites in two additions with a rubber spatula, being careful not to overmix and deflate the batter.
Bake the Soufflé: Generously butter a 2-quart soufflé dish. Carefully pour the soufflé mixture into the prepared dish.
Place it in a preheated 350°F / 175°C oven and bake for 35 to 40 minutes, or until the soufflé is puffed, golden brown, and set.
Do not open the oven door for the first 30 minutes.
Serve immediately with a light tomato sauce on the side.
