Preheat the oven to 375°. Butter a 1 1/2-quart soufflé dish and coat it with 2 tablespoons of the Parmigiano.
In a medium saucepan, melt the butter. Stir in the flour to make a paste. Gradually whisk in the cream and bring to a boil over moderate heat, whisking. Reduce the heat to low and cook, whisking, until very thick, 3 minutes. Transfer the base to a large bowl; let cool. Stir in the egg yolks, sherry, Gruyère, sour cream, salt, Dijon mustard, dry mustard, cayenne and the remaining 1/4 cup of Parmigiano.
Put the 7 egg whites in a large stainless steel bowl. Add the cream of tartar. Using an electric mixer, beat the whites until firm peaks form. Fold one-third of the whites into the soufflé base to lighten it, then fold in the remaining whites until no streaks remain.
Scrape the mixture into the prepared dish. Run your thumb around the inside rim of the dish to wipe away any crumbs. Bake for about 35 minutes, until the soufflé is golden brown and puffed. Serve right away.