Whisk the eggs with black pepper until the mixture is uniformly yellow, but do not beat any air into it. Omit the salt: the smoked trout is already salty enough, and adding salt to raw eggs too early draws moisture from the yolks, which can cause the scrambled eggs to curdle later.
Melt the butter in a heavy-bottomed skillet over low heat and pour in the eggs as soon as the butter foams but before it colors. Wait half a minute, then gently sweep a spatula from the edge to the center. Keep sweeping and sliding rather than stirring; this creates large, soft curds instead of small grains.
Remove the pan from the heat when the eggs still look distinctly wet. The pan retains enough heat to finish cooking the dish in the final twenty seconds, which is exactly the difference between creamy and dry.
Stir in the crème fraîche and lemon zest off the heat. The cold cream abruptly stops the cooking process and makes the texture silky smooth.
Flake the smoked trout into large pieces and gently fold them in, so the fish warms through without cooking further.
Spoon the scrambled eggs onto a plate with the watercress on the side, and sprinkle with plenty of finely snipped chives and black pepper. Three eggs with trout provide over twenty-five grams of protein and virtually no carbohydrates.