In a pot, heat the olive oil over medium heat. Add onion, carrot, and celery. Sauté until softened, about 5–6 minutes.
Pour in the chicken broth, cooked chicken, salt and pepper. Bring to a simmer. Cover and cook for 10 minutes to let the flavors come together.
While the soup simmers, stir together the flour, baking powder, salt, and herbs in a small bowl. Add the milk and melted butter and stir just until combined. The dough will be thick—don’t overmix.
Uncover the soup and drop heaping spoonfuls of the dumpling dough directly onto the simmering liquid. You should get 4–5 small dumplings. Cover the pot and simmer for 12–15 minutes, or until the dumplings are puffed and cooked through. Don’t lift the lid too early—dumplings like their steam.
Stir in the peas and a splash of cream, if using. Taste and adjust seasoning. Serve hot.