Brown the chicken in vegetable oil in a large pot or Dutch oven. Work in batches to avoid overcrowding.
Add onion, celery, and carrots to the pot and cook until softened, about 5-7 minutes.
Add garlic, chicken broth, bay leaf, thyme, and rosemary. Bring to a simmer.
Season with salt and pepper to taste.
Simmer for 1 hour, or until the chicken is cooked through.
Remove the chicken from the pot and shred the meat. Discard the skin and bones. Return the shredded chicken to the pot.
Remove the bay leaf.
While the chicken is simmering, prepare the dumplings. In a large bowl, whisk together flour, baking powder, and salt.
Cut in shortening or butter until the mixture resembles coarse crumbs.
Gradually add milk or buttermilk, mixing just until the dough comes together. Do not overmix.
Drop spoonfuls of dumpling dough into the simmering broth.
Cover the pot and cook for 15-20 minutes, or until the dumplings are cooked through and fluffy.
Garnish with fresh parsley, if desired.
Serve hot and enjoy!