Heat a large pot of salted water to a boil. Cook the pasta according to package directions – but one minute before the pasta is tender, add the sugar snap peas and the asparagus. Cook for one minute, then drain the pasta and the vegetables and rinse under cold water. Drain well.
Place the pasta, sugar snap peas, and asparagus in a bowl with the arugula, spinach, peppers, tomatoes and scallions.
In a small bowl or container combine the olive oil, mayonnaise, vinegar, mustard, shallots, basil, salt and pepper. Pour the dressing over the pasta salad and toss well to combine. Add the Parmesan and toss again. Taste and adjust the seasonings as needed.