Finely mince the half onion. Cut the half bell pepper into small cubes and slice the fifty grams of mushrooms into thin slices. Whisk the three eggs vigorously in a bowl and add a pinch of salt and pepper to taste, if desired.
Heat a little butter in a skillet over medium-high heat. Sauté the minced onion for a few minutes until it becomes translucent. Add the bell pepper cubes and sliced mushrooms to the pan and cook everything through until the vegetables are soft and most of the liquid has evaporated.
Pour the whisked eggs evenly over the vegetable mixture in the pan. Reduce the heat slightly to prevent the bottom from burning. Let the egg mixture set gently and lift the edges occasionally with a spatula, allowing the liquid egg to flow toward the hot bottom. Cook until the top of the omelette is completely set and firm.
Gently slide the farmer's omelette from the skillet onto a flat plate. Fold the omelette in half or cut it into large wedges and serve immediately.