Melt the butter in a large pot over medium heat.
Add the onion, carrots, and celery, and sauté until softened, about 5 minutes.
Stir in the garlic, thyme, rosemary, pepper, and salt, cooking for another minute until fragrant.
Pour in the chicken broth and bring to a boil.
Reduce heat to a simmer and add the shredded chicken and frozen peas.
Stir in the heavy cream and let simmer for 10 minutes.
In a separate bowl, combine the flour, baking powder, and salt.
Add the melted butter and milk, stirring until just combined. The dough will be thick.
Drop spoonfuls of the dumpling dough into the simmering chicken mixture.
Cover the pot and cook for 15-20 minutes, or until the dumplings are fluffy and cooked through. Avoid lifting the lid during cooking.
Serve hot, garnished with fresh herbs if desired.