Sauté the vegetables: Melt the butter over medium heat in a Dutch oven or stockpot. Add chopped onion, celery, and carrots, and sauté for 4-5 minutes until fragrant.
Add garlic and seasonings: Stir in minced garlic, dried parsley, and poultry seasoning. Cook for 1 minute, stirring constantly.
Thicken the soup: Sprinkle 1 ½ tablespoons of flour over the vegetables and stir for 1 minute.
Simmer: Add the chicken broth and bay leaf, bringing the mixture to a simmer. Let it cook for 25 minutes.
Add chicken and peas: Remove the bay leaf, season with salt and pepper to taste, then add the cooked chicken and frozen peas. Simmer for an additional 5 minutes.
Make dumpling batter: In a medium bowl, mix flour, baking powder, sugar, and salt. Cut in butter until the mixture is crumbly. Stir in milk until just combined.
Cook dumplings: Drop small spoonfuls of dumpling batter into the simmering soup. Cover and cook for 15 minutes without removing the lid.
Serve: Ladle the soup into bowls, ensuring each serving has chicken, vegetables, and dumplings. Serve hot.
