Crack the eggs into a bowl.
Grind salt and pepper into the egg mixture and add the cayenne pepper.
Whisk everything together well.
Put a small pot/saucepan on the stove and turn on to medium heat (6-7 out of 14 on my stove).
Add half of the butter and let it melt.
When it starts to sizzle, add the egg mixture. Use a spatula to get everything in.
Stir the eggs so they don't stick to the bottom. Start by stirring well and make sure you get everything from the edges. It's like making a risotto; you have to stir constantly.
After about 1 minute, start pushing the egg mixture towards the center.
It will slowly start to come together, and when most of the mixture has thickened, take it off the heat.
Add the other half of the butter and mix it well into your scrambled eggs.
Serve with toasted bread and optionally ham, bacon, smoked salmon, or just chopped chives.
Serve the dish immediately.
Bon appétit.