Melt the butter in a small saucepan over a moderate heat until it’s foaming.
Whisk the eggs in a bowl and add to the saucepan. Stir the eggs continuously with something flexible like a spatula to get right into the corners, and cook until little pieces of cooked egg are surrounded by soft, smooth and still quite runny egg. The egg will continue to cook even when the heat is turned off, so undercook them slightly and leave them in the pan while you butter your toast.
Season the eggs with sea salt and freshly ground black pepper to taste and pour over the toast.
Quarter the lemon, then drape the salmon over the eggs and serve it with the lemon wedges. Add plenty of black pepper and serve immediately.