Heat the olive oil in a large skillet over medium-high heat. Add the asparagus, mushrooms and onions; cook and stir until the asparagus is fairly soft, about 4 minutes. Whisk together the eggs and milk in a small bowl; pour over the sauteed vegetables and reduce the heat to medium. While the omelet cooks, lift the edge to allow the uncooked egg to flow underneath. When most of the egg is cooked, sprinkle Parmesan cheese over the top. Allow the cheese to melt slightly, then fold in half and serve.