Sauté the aromatics. In a large pot or Dutch oven, heat butter and olive oil over medium heat. Add onion, carrots, and celery. Cook 6–8 minutes until softened.
Stir in garlic and cook 30 seconds until fragrant.
Build the broth. Pour in chicken broth, add bay leaf, salt, pepper, and poultry seasoning. Bring to a gentle simmer.
Add the chicken. Stir in shredded chicken. Simmer 10 minutes to let flavors come together.
Taste and adjust seasoning.
Make the dumpling dough. In a bowl, whisk flour, baking powder, salt, and baking soda. Cut in cold butter with your fingers or a pastry cutter until it looks like coarse crumbs. Stir in buttermilk just until a soft, slightly sticky dough forms.
Do not overmix.
Drop the dumplings. Reduce the soup to a steady simmer (not a rolling boil). Using a spoon or small scoop, drop tablespoon-sized mounds of dough onto the surface, leaving a little space between each.
Steam, don’t stir. Cover the pot with a tight lid. Cook 12–15 minutes without lifting the lid.
The dumplings will puff and cook through from the steam. Check one: it should be set and fluffy in the center.
Finish the soup. Remove the bay leaf. Stir in cream and parsley.
Gently nudge the dumplings around to coat with broth, but don’t break them up. Simmer 2 more minutes. Taste and season with additional salt and pepper as needed.
Serve. Ladle into bowls with plenty of broth and a couple of dumplings each.
Sprinkle more parsley if you like.