In a large pot or Dutch oven, combine the chicken, onion, carrots, parsley, bay leaves, salt, pepper, saffron, and garlic powder. Add enough water to cover the chicken.
Bring to a boil, then reduce heat and simmer for 45-60 minutes, or until the chicken is cooked through and tender.
Remove the chicken from the pot and shred or dice it. Discard the bay leaves.
In a separate bowl, combine the flour and poultry seasoning. Cut in the shortening until the mixture resembles coarse crumbs.
Gradually add the milk to the flour mixture, stirring until just combined. Do not overmix.
Drop spoonfuls of the dough into the simmering broth. Cover and cook for 15-20 minutes, or until the dumplings are cooked through.
Return the shredded chicken to the pot and heat through. If desired, thicken the broth with a slurry of cornstarch and water.
Season with salt and pepper to taste. Serve hot.