Ramekins must be spotless prior using. Grease ramekins with a thick coating of softened butter and flour; remove excess flour. Refrigerate prepared ramekins until ready to use.
Melt butter in heavy saucepan over medium heat. Add flour and whisk until mixture begins to foam and loses raw taste, about 2 minutes. Remove saucepan from heat. Pour in cold milk at once whisking until smooth. Return to heat and cook for 2 minutes. Remove from heat, and season with salt, pepper and nutmeg. Incorporate egg yolks swiftly, shredded cheese and vin jaune, cover and set aside. Turn oven on. Meanwhile, in a stand mixer fitted with the whisk attachment, beat egg whites with a pinch of salt to medium-firm peaks. Immediately fold one-third of the egg whites into the soufflé mixture, then the remaining. Spoon half of the mixture into the ramekins and add the cubed cheese. Fill up with remaining mixture to come 0.11''/3mm above the rim. Smooth out the surface with an offset spatula, then run the tip of your thumb to ease the mixture away from the side of each ramekin to help it rise.
Set the oven rack adjusted to the lower-middle position with a large baking tray and preheat oven to 400ºF/205ºC. Lower temperature to 375ºF/190ºC if using a convection oven. Transfer the ramekins on the hot baking tray and bake until soufflé is puffed and golden brown on top, about 15 minutes – do not open oven door during baking! – Put the cooked soufflés on individual plates and serve at once - they won't wait!