In a large Dutch oven, add the chicken, broth, carrots, celery, onion, garlic, salt, pepper, thyme, and bay leaf.
Bring to a boil over medium-high heat, then reduce to a simmer. Cover and cook for about 45 minutes, or until the chicken is tender and easily falls off the bone.
Remove the chicken and let it cool slightly. Shred the meat, discarding the bones and skin.
Return the shredded chicken to the pot. Stir in the heavy cream if using.
Make the Dumplings
In a mixing bowl, whisk together flour, baking powder, salt, and baking soda.
Stir in buttermilk and melted butter until just combined. The dough should be soft but not too sticky.
For drop dumplings: Scoop spoonful of dough and drop them directly into the simmering broth.
For rolled dumplings: Roll the dough out to about ¼-inch thickness, then cut into squares before adding to the broth.
Cook the Dumplings
Cover the pot and let the dumplings cook for about 15 minutes over low heat, without stirring. This allows them to steam and become light and fluffy.
Check for doneness by cutting a dumpling in half—if it’s cooked through, you’re good to go!
Serve and Enjoy
Remove the bay leaf, ladle the chicken and dumplings into bowls, and enjoy this cozy, heartwarming dish.