Crack the three organic eggs into a bowl and beat them well with a fork. Add freshly ground pepper and a small pinch of Celtic sea salt. Be sparing with the salt, since the smoked trout already has a salty flavor of its own. Chop the fresh chives into fine pieces and set aside.
Heat the teaspoon of coconut oil in a skillet over medium-high heat. Add the wild spinach once the oil is warm and toss briefly until the leaves just begin to wilt. Then pour the beaten egg mixture over the spinach and distribute the pieces of smoked trout evenly across the pan.
Reduce the heat to low and cover the skillet with a lid. Let the omelette set gently this way for about five minutes. Check that the top of the egg mixture is completely dry and cooked through before removing the pan from the heat.
Sprinkle the hot omelette with the finely chopped fresh chives. Carefully slide the dish from the pan onto a plate, fold the omelette in half with a spatula, and serve immediately.