Beat the eggs lightly in a bowl with a pinch of salt and pepper. Heat the olive oil in a frying pan over medium-high heat and add the spinach; stir until the leaves have just wilted.
Pour the egg mixture over the spinach and let it set gently. Using a spatula, pull the edges toward the center occasionally so the liquid egg flows to the sides.
Once the top is almost set, crumble the goat cheese over one half of the omelet. Fold the other half over it and let it cook gently for another half minute until the cheese begins to melt. Slide the omelet onto a plate and grind some more pepper over it.