Whisk rice wine vinegar, soy sauce, red wine vinegar, lime juice, sugar, pressed garlic, and salt in a small bowl.

Gradually whisk in vegetable oil until emulsified.

Cover the dressing and let it stand at room temperature for up to 1 day.

Rewhisk the dressing before using.

Cook Chinese egg noodles according to package directions.

Drain the noodles and refresh under cold water, then drain again.

Transfer the noodles to a large bowl and toss with 1/4 cup (or less) of oil.

Heat the remaining 1/4 cup (or less) of oil in a large heavy skillet over high heat.

Add all mushrooms and cook until just barely tender, about 4 minutes.

Pour off any excess oil and add the mushrooms to the noodles.

Toss the noodles with enough dressing to season to taste.

Let stand for 2 hours at room temperature or prepare 1 day ahead and bring to room temperature before continuing.

Cook snow peas in a large pot of boiling water for 30 seconds.

Drain the snow peas and refresh under cold water, then drain again.

Add the peas, bean sprouts, green onions, and 2 tablespoons of sesame seeds to the noodles and toss gently.

Sprinkle the remaining 1 tablespoon of sesame seeds over the noodles and serve.