Place the chicken stock in a small saucepan and warm over low heat.
In a large pot or Dutch oven, melt the butter over medium-low heat. Add the onion, carrot, and celery and saute until the onion is translucent, 10 to 15 minutes. Add the garlic and cook for an additional 1 minute. Add the flour and cook for 2 minutes, stirring constantly.
Slowly add the hot chicken stock, stirring constantly, and simmer over low heat until thickened, about 1 minute. Stir in the heavy cream, salt, pepper, thyme and bay leaves. Adjust the heat to maintain a slow simmer while you prepare the dumplings.
Make the Dumplings: In a medium bowl, whisk together the flour, baking powder, and salt. Add the melted butter and milk and stir with a rubber spatula until the dough just comes together.
Stir the chicken, peas, and parsley into the pot. Drop the dumpling mixture by large spoonfuls of dough over the surface of the chicken stew. Cover and cook for 15 minutes. Check the dumplings with a toothpick to see if they’re done; if they are still doughy in the middle, flip them over, cover and simmer for an additional 5 minutes. Serve immediately.