Preheat the oven to 375 degrees Brush the interior of a 6-cup soufflé mold with the softened butter.
Cut the eggplant in half lengthwise. Place on a baking sheet. Brush eggplant with a teaspoon of olive oil.
Bake 20 to 30 minutes or until eggplant is soft to touch. Remove the eggplant from the oven. Scrape away the inner pulp and discard The skin. Chop the pulp. There should be about a cup. Cover and set aside.
In a heavy saucepan heat the remaining oil. Add the onions and garlic. Cook briefly while stirring, until onions are wilted. Stir in the flour and cornstarch. Add the milk. Cook while whisking until sauce becomes thick. Tranfer the Bubbly sauce to a large mixing bowl. Season with salt and pepper and chopped parsley. Mix egg yolks, and eggplant pulp into the thick cream sauce.
Using an electric beater, whip the egg whites and cream of tartar until stiff And glossy. Do not overbeat. Gently fold into cream sauce mixture. Pour and scrape the mixture into the prepared soufflé mold.
Place on a baking sheet. Cook in the middle of the oven for 20 to 30 minutes. Heat marinara sauce or tomato sauce. Serve with the soufflé.