Add chicken, crushed tomatoes, carrots, celery, garlic, farro, broth, olive oil, and spices to a large pot or pressure cooker.
Cook until the chicken is tender and the grains are fully cooked (about 20–25 minutes on stovetop or 20 minutes in pressure cooker).
Remove the chicken, shred it, and return it to the pot.
Add zucchini and corn, then cook for another 5–10 minutes until tender.
Let the soup rest for a few minutes to thicken slightly.
Taste and adjust seasoning as needed.
Serve warm with your favorite toppings.