Combine first 6 ingredients in a small bowl, stirring well. Set aside.
Snap off tough ends of asparagus. Remove scales from spears with a knife or vegetable peeler, if desired. Cut asparagus into 1-inch pieces. Arrange asparagus in a vegetable steamer over boiling water. Cover and steam 4 to 5 minutes or until crisp-tender. Rinse with cold water.
Break spaghetti in half; cook according to package directions, omitting salt and fat. Drain; rinse with cold water, and drain. Place spaghetti in a bowl. Add vinegar mixture, asparagus, peas, and sweet red pepper; toss well. Sprinkle with cheese, and top with cherry tomato quarters. Cover and chill thoroughly.