Bring a large saucepan of lightly salted water to a boil. Add the egg noodles and cook briefly until just tender, about 5 minutes. Drain thoroughly.
Thinly slice the red onion and the shitake mushrooms. Preheat a wok, or heavy skillet, and add the vegetable oil and swirl it around. When the oil is hot, add the onion and mushrooms, and stir fry for 3 minutes.
Add the noodles to the wok with the soy sauce, balsamic vinegar, brown sugar and salt. Toss them over the heat for 3 minutes. Add the sesame oil. Transfer to a warmed bowl, and serve at once, garnished with the parsley leaves, if desired.