Brown the chicken in a large pot or Dutch oven. Work in batches to avoid overcrowding.
Add the onion, carrots, and celery to the pot and sauté until softened, about 5-7 minutes.
Pour in the chicken broth and add the thyme, rosemary, and bay leaf. Bring to a simmer.
Reduce heat to low, cover, and simmer for 1 hour, or until the chicken is cooked through.
Remove the chicken from the pot and shred it with two forks. Return the shredded chicken to the pot.
In a separate bowl, whisk together the flour, baking powder, and salt for the dumplings.
Cut in the shortening using a pastry blender or your fingers until the mixture resembles coarse crumbs.
Stir in the milk until just combined. Do not overmix.
Drop spoonfuls of the dumpling dough into the simmering broth.
Cover and simmer for 15-20 minutes, or until the dumplings are cooked through.
Stir in the heavy cream and season with salt and pepper to taste.
Remove the bay leaf before serving. Serve hot and garnish with fresh parsley, if desired.
