Heat a large Dutch oven over medium heat and add the chicken pieces. Cook until lightly browned on all sides, then remove the chicken to a plate.
Add the onion, carrots, and celery to the same pot. Cook for 5 minutes until the vegetables begin to soften.
Sprinkle the 1/4 cup flour over the vegetables and stir for 1 minute to form a light roux.
Slowly pour in the chicken broth while stirring. Return the chicken to the pot, add the thyme, salt, and pepper, then bring to a simmer.
Stir in the heavy cream and let the mixture cook gently for 10 minutes.
In a mixing bowl, combine the 1 1/2 cups flour, baking powder, and 1/2 teaspoon salt. Add the milk and melted butter, then stir just until a soft dough forms.
Drop spoonfuls of the dumpling dough onto the simmering stew. Cover the pot and cook for 12 minutes without lifting the lid so the dumplings steam through.