Grease six (6 oz) ramekins with 1 tablespoon (½ oz/14g) of butter. Add some grated parmesan to the dishes, rotating ramekins all around so cheese sticks to every part of the buttered surface. Tap out any excess before transferring the prepared ramekins to the refrigerator until ready to use.
In a medium saucepan, melt 3 tablespoons (1 ½ oz/43 g) butter over medium low heat. Add the thinly sliced leeks and gently saute for 2 to 3 minutes without coloring.
Add flour and whisk to form a paste. Continue to cook, stirring, about 1 minute. Whisking constantly, add milk in a thin, steady stream, whisking thoroughly and getting into the sides of the pan to maintain a lump-free texture.
Cook gently until the sauce is thickened, about 1 to 2 minutes. Season generously with salt and pepper and the Dijon mustard. Transfer béchamel sauce to a large bowl and allow to cool slightly.
Whisk in egg yolks one at a time until thoroughly blended. When the base is cool, cover and place it in the fridge until needed. Note: This soufflé base can be made up to 2 days in advance and held in the fridge.
Preheat the oven to 400ºF (200ºC). Make sure there is room for your soufflés to bake as they rise up high in the oven.
In a large mixing bowl of a stand mixer fitted with a whisk attachment or using an electric hand mixer, combine egg whites with cream of tartar and whisk on medium low speed for 2 minutes, until foaming.
Turn up the speed to high and whisk until stiff peaks form, around 4 minutes.
Using a metal spoon, add ⅓ of the egg whites to the béchamel base and fold in to loosen the mixture.
Add in the remaining whites and fold until whites are combined. Lastly, fold in the Gruyère.
Remove the soufflé ramekins from the refrigerator and set on a baking sheet. Scoop soufflé batter into the prepared baking ramekins, filling it up to the top. Using an offset spatula, gently smooth and level surface of the soufflé batter.
Transfer soufflé to the oven and bake until well risen and nicely browned on top, 18 to 20 minutes. Note: take care not to over bake, you want an oozy, almost gooey cheesy center.
Immediately transfer soufflés to the table and serve hot from the oven.