In a large Dutch oven or heavy pot, melt 3 tablespoons butter over medium heat. Add onion, celery, and carrots, cooking for 6-8 minutes until vegetables are softened.
Sprinkle ⅓ cup flour over the vegetables and stir well, cooking for 2-3 minutes to create a roux.
Gradually pour in chicken broth while whisking constantly to avoid lumps. Add thyme, poultry seasoning, salt, and pepper.
Bring the mixture to a boil, then reduce heat to medium-low and simmer for 10 minutes.
Meanwhile, make the dumplings by whisking together 2 cups flour, baking powder, and 1 teaspoon salt in a medium bowl. Stir in milk and melted butter just until combined (don't overmix).
Drop dumpling batter by rounded tablespoons into the simmering soup. Cover and cook for 15 minutes without lifting the lid.
Gently stir in the cooked chicken and heavy cream. Heat through for 3-5 minutes.
Taste and adjust seasonings as needed. Serve hot with extra black pepper if desired.