Bring a large pot of water with the tablespoon salt to a boil. Cook tortellini according to its package until tender, adding asparagus during the last 2 minutes.
Drain gently, rinse briefly under cool water and leave in the colander for 5 minutes to remove water held in the 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 until coated, keeping the tortellini intact. Serve cool or cover and refrigerate promptly for 30 minutes.
Toss lightly before serving and refrigerate leftovers within 2 hours.