In a small bowl combine mushrooms and boiling water. Cover and let stand for 20 minutes. Drain mushrooms, squeezing out excess liquid; reserve 1/2 cup liquid. Chop mushrooms and set aside. Meanwhile, cook noodles in additional boiling water for 5 minutes; drain and return to saucepan.

For egg strips, combine egg whites and egg. In a 10-inch nonstick skillet heat 1 teaspoon of the cooking oil and 1 teaspoon of the sesame oil over medium heat until hot. Pour egg mixture into skillet. Lift and tilt the skillet to form a thin layer of egg on the bottom. Cook, without stirring, for 2 or 3 minutes or until just set. Slide egg mixture out onto a cutting board; cool slightly and cut into 2x1/2-inch-long strips. Set aside.

In the same skillet heat the remaining 1 teaspoon cooking oil and 1 teaspoon sesame oil over medium-high heat. Add mushrooms, garlic, ginger, and, if desired, crushed red pepper. Cook and stir for 1 minute. Add sweet pepper and peas; cook and stir 2 minutes more. Add reserved mushroom soaking liquid and teriyaki sauce. Bring to boiling; boil gently, uncovered, for 3 minutes. Add egg strips and vegetable mixture to noodles; toss well. Serve immediately. Makes 4 (1 1/4-cup) servings.