Preheat the oven to 400°F and position the rack in the center. Lightly butter the bottoms and sides of 8, 6-ounce ramekins or custard cups. Dust the dishes with the parmesan cheese (so that it adheres to the butter) and knock out the excess.
In a small bowl, whisk together the salt, mustard, black pepper, and cayenne in a small bowl. Set aside.
Warm the milk (do not boil it) in a medium saucepan over medium heat. Remove from the heat once tiny bubbles appear.
Melt the butter in a medium heavy-bottomed saucepan. Add the flour and whisk until completely combined, about 2 to 3 minutes. Remove from the heat and then slowly stream the milk into the butter mixture while whisking constantly. Continue whisking until smooth, and return to the heat. Cook until the mixture bubbles and becomes thick, about 8 to 10 minutes. When bubbles appear, remove from the heat and whisk in the spice mixture. Continue stirring vigorously for about 1 minute to release some of the heat. Add the 6 egg yolks, one at a time, whisking after each addition. After all the yolks are completely incorporated, transfer the mixture to a large bowl.
Whisk the 6 egg whites vigorously for 1 minute in another large bowl (or in the bowl of a stand mixer fitted with the whisk attachment). Sprinkle the cream of tartar over the whites and continue beating until the egg whites form stiff peaks.
Fold one-third of the egg white mixture into the soufflé base. Add the Cheddar cheese and corn, along with half of the remaining egg whites, and gently fold until almost incorporated. Gently fold in the remaining egg whites until completely but just incorporated.
Evenly divide the mixture between the prepared ramekins. Run your thumb around the inside edges of the dishes to wipe away any stray mixture (this will help with an even rise), place the soufflés in the oven, and immediately reduce the oven temperature to 375°F. Bake for 25 to 30 minutes or until the soufflés are puffed and golden and the center is just set. Transfer the soufflés to serving plates and serve immediately.