Whisk the eggs in a bowl with a pinch of salt and pepper. Brush the mushrooms clean and slice them.
Heat the olive oil in a skillet over medium-high heat and fry the mushrooms golden brown in a few minutes. Add the spinach and stir until the leaves are just wilted.
Pour the egg mixture over the vegetables and let it set gently; pull the edges toward the center from time to time so the liquid egg flows to the sides. Crumble the goat cheese over one half as soon as the top is almost set, fold the other half over it and let cook for another half minute until the cheese melts. Slide the omelette onto a plate and grind some pepper over it.