1In 2-quart saucepan, heat oil over medium-high heat. Add onion and bell pepper to oil; cook about 5 minutes, stirring frequently, until onion is tender. Stir in mushrooms and garlic; cook about 5 minutes, stirring frequently, until mushrooms are tender and liquid evaporates. Add remaining sauce ingredients; reduce heat. Cover; simmer, stirring occasionally, while preparing noodles.
2In 3-quart saucepan, heat 2 quarts water to boiling. Add noodles. Cook 2 to 3 minutes; drain. On heatproof plate lined with paper towels, place noodles (to prevent them from sticking together). Divide warm noodles evenly among 6 bowls. For each serving, top noodles with 1 cup sauce and sprinkle with 2 teaspoons Parmesan cheese.