Pour the beaten eggs into the pan. Keeping the heat on medium, allow the eggs to cook undisturbed until just a little wet on top (3 to 4 minutes).
Sprinkle the cheese over the eggs. Arrange the arugula and mushrooms on just one side of the eggs. Continue cooking another minute or so just until the eggs have set. Gently flap over the eggs to cover the mushroom side of the omelette. Serve hot.