Prepare instant noodles by covering with boiling water and stirring occasionally, separating noodles until al dente, from 4 to 6 minutes. Then drain and set aside. If using rice noodles, soak in hot water for 15 minutes. Drain and set aside. Or cook spaghettini in salted boiling water according to package directions. Drain well and set aside.
In a measuring cup or small bowl, stir hoisin sauce with soy sauce, vinegar, ginger, garlic, sugar and 1/2 cup (125 mL) hot water until well mixed. Set aside. Slice steak into bite-size strips and set aside in a medium-size bowl. Remove mushroom stems, slice off soil-covered ends and discard. Thickly slice stems and caps. Seed pepper and cut into 1-inch (2.5-cm) pieces. Diagonally slice onions into 3/4-inch (2-cm) pieces.
Heat 1 tablespoon (15 mL) oil in a large wide frying pan or wok set over high heat until very hot. Add steak and stir constantly until steak just starts to brown, no more than 2 minutes. Remove to a plate. Add remaining tablespoon (15 mL) oil to pan, then add mushrooms and 1/4 cup (50 mL) water. Stir constantly for 2 minutes. Add pepper and stir-fry for 1 minute.
Immediately pour in hoisin mixture. Add all of drained noodles, steak, including any accumulated juices, and onions. Toss constantly until noodles are hot and have absorbed some sauce, about 3 minutes. Serve immediately.