Make the base – In a large pot, melt butter and sauté onion, carrots, celery, and garlic until softened (about 5 minutes).
Add broth & chicken – Pour in chicken broth, thyme, bay leaf, salt, and pepper. Stir in shredded chicken. Simmer for 15 minutes.
Mix dumplings – In a bowl, whisk flour, baking powder, salt, pepper, and parsley. Stir in milk and melted butter until just combined (dough will be sticky).
Add dumplings – Drop spoonfuls of dough into the simmering soup. Cover and cook 15 minutes without lifting the lid (steam cooks the dumplings).
Finish – Stir in peas and cream (if using). Adjust seasoning. Serve hot with fresh parsley on top.