Make the Soup Base:
Heat olive oil or butter in a large pot over medium heat. Sauté the onion, carrots, and celery until softened, about 5 minutes. Add garlic and cook for 1 minute.
Thicken the Broth:
Sprinkle flour over the vegetables and stir to coat. Gradually pour in chicken broth, stirring constantly to avoid lumps.
Simmer the Soup:
Add shredded chicken, thyme, rosemary, salt, and pepper. Bring to a boil, then reduce heat to a simmer. Stir in heavy cream if using.
Prepare the Dumpling Batter:
In a mixing bowl, combine flour, baking powder, and salt. Stir in milk and melted butter until a thick batter forms.
Add Dumplings:
Drop spoonfuls of dumpling batter onto the simmering soup, making sure they don’t touch. Cover the pot and let the dumplings cook for 10-15 minutes without lifting the lid, until they are fluffy and cooked through.
Finish and Serve:
Ladle the soup into bowls, ensuring each serving gets plenty of dumplings. Serve warm and enjoy!