Cook the pasta according to package instructions. Drain and rinse with cold water to stop the cooking process.
Leave pasta in the strainer until ready to use.
In a large bowl, whisk together soy sauce, vegetable oil, sugar, salt, black pepper and sesame oil until smooth. Add garlic and rice vinegar. Whisk until combined.
Pour 1/4 cup of the dressing from the large bowl into a smaller bowl. Add mushrooms, red pepper and peas. Toss to coat.
Pour pasta into the large bowl with dressing and toss until evenly coated. Fold in vegetables. Serve topped with green onions and drizzled with extra dressing if desired.