Fill a large pot with water, bring to a rolling boil over high heat, then add a pinch of salt.

Add the egg noodles and cook for 3 to 4 minutes if fresh or 5 to 6 minutes if dried.

Drain noodles in a colander without rinsing; toss with a light drizzle of oil if not cooking immediately.

While noodles cook, shred cabbage, dice carrots, slice mushrooms, chop green onions into 1-inch pieces, and mince garlic and ginger.

In a small bowl, whisk together soy sauce, oyster sauce, sesame oil, rice vinegar, sugar, white pepper, and chicken broth until sugar dissolves.

Heat a wok or large skillet over high heat until a drop of water sizzles and evaporates, about 1 minute.

Add 1 tablespoon vegetable oil to the hot wok, then add garlic and ginger and stir for 20 seconds until fragrant.

Add carrots and mushrooms and stir-fry for 2 minutes, then add cabbage and green onions and cook for 1 to 2 minutes until tender-crisp.

Add drained noodles and remaining 1 tablespoon vegetable oil; toss for 30 seconds, then pour in sauce and toss for 1 to 2 minutes until noodles are glossy and coated.

Remove wok from heat, taste, and adjust seasoning with additional soy sauce or sesame oil before serving.