Preheat your oven to 200°C (180°C fan). Grease the insides of 6 ramekins with butter, then coat with breadcrumbs.
Melt the butter in a saucepan over medium heat. Stir in the flour and cook for 1 minute to make a roux.
Gradually whisk in the milk until you have a smooth sauce. Cook for 2-3 minutes, stirring constantly, until thickened.
Remove from heat and stir in the grated cheese, mustard, cayenne (if using), and season with salt and pepper. Allow the mixture to cool slightly before beating in the egg yolks.
In a clean bowl, whisk the egg whites to medium peaks. Gently fold a third of the whites into the cheese mixture to lighten it, then carefully fold in the rest, keeping as much air as possible.
Pour the mixture into the prepared ramekins, filling them about two-thirds full. Run your thumb or a knife around the edges to create a slight indent—this helps it rise evenly.
Place the ramekins on the hot baking tray (to give them an immediate burst of heat) in the top of the oven and bake for 8–12 minutes until well risen and cooked, but still uniformly wobbly when lightly shaken. Serve immediately. There should be about 1 tsp undercooked soufflé mixture in the center.
To make a large soufflé (to serve 2–3 as a main course), put the mixture into a 15cm soufflé dish instead of individual ones and bake for 25–30 minutes.