Bring a large pot of salted water to a boil and cook the pasta according to the directions on the package. During the last two to three minutes of the cooking time, add the frozen peas. Immediately drain the pasta and peas, and rinse in cold water.
In a large bowl, combine the pasta, peas, celery, red pepper and onion. In a small bowl, whisk together the mayonnaise, vinegar, basil, mustard, salt and pepper. Pour the dressing over the pasta mixture and toss to coat. Cover and refrigerate for at least one hour to allow all the flavors to marinate before serving.
