Melt the butter in a saucepan over a gentle heat until foaming.
Put the eggs in a bowl and mix well with a fork. Add the milk and season with salt and pepper.
Pour the eggs into the foaming butter and cook, stirring constantly with a wooden spoon, scraping the bottom of the pan and bringing the eggs from the outside to the centre. The eggs are done when they form soft, creamy curds and are barely set.
Remove the pan from the heat and stir in the cream, if using, salmon and chives. Pile on to the hot toast on a warmed serving plate. Serve immediately.