To make the zucchini or diakon into “noodles,” peel and cut the zucchini into noodle shapes using either a spiral slicer or a vegetable peeler. Set the noodles aside.
In a stockpot, heat the butter over medium-high heat. Add the cubed chicken, celery, and onions and sauté until the veggies are soft, about 7 minutes.
Add the broth, ginger (if using), parsley, salt, pepper, marjoram, and bay leaf. Simmer, uncovered, for 10 minutes, or until the chicken is no longer pink inside.
Add the noodles and simmer for 3 more minutes.
Remove from the heat, remove the bay leaf, and serve. Store in an airtight container in the refrigerator for up to 5 days. If you plan to freeze the soup, do not add the noodles (either type) until you reheat it.