Bring a large pot of water with tablespoon salt to a boil. Cook tortellini to package directions until tender, adding asparagus for last 2 minutes.
Drain gently; rinse briefly under cool water. Drain in colander 5 minutes to release water from pasta folds.
Whisk oil, lemon juice, zest, Dijon, dressing salt, and pepper in a large bowl. Add tortellini, asparagus, thawed peas, and parsley.
Fold gently with a wide spoon to coat without breaking tortellini. Serve cool, or cover and refrigerate promptly 30 minutes.
Toss lightly before serving; refrigerate leftovers within 2 hours.