Combine the chicken broth and celery in a large saucepan, bring to a boil and simmer until the celery is tender-crisp, 3-4 minutes; remove from the heat, add the Parmigiano Reggiano, stir, cover and set aside.
Cook the tortelloni according to the package instructions and drain, reserving 1/2 cup of the pasta cooking water. Add the pasta to the celery-parmesan mixture in the skillet along with the crème fraîche and parsley. Bring the mixture to a low boil once more, cook for 1 minute and season with salt and pepper to taste. Divide among plates and garnish with additional parsley, if desired.