Place the turkey carcass in a large stockpot and cover it with water. Bring to a boil.
Reduce the heat to a simmer and skim off any foam.
Add onion, carrots, celery, garlic, bay leaves, thyme, and a pinch of salt. Let it simmer for 2–3 hours.
Strain the broth through a fine-mesh sieve into a large bowl, discarding the solids.
Return the broth to the pot, add rice, noodles, or barley, and cook until tender.
Season with salt and pepper to taste. Garnish with parsley and serve.