01 - Heat olive oil in a large pot over medium heat. Add diced onion, carrots, and celery; sauté for 5 minutes until vegetables are softened and translucent.
02 - Stir in minced garlic, dried thyme, dried parsley, bay leaf, salt, and black pepper. Cook for 1 minute until the mixture becomes fragrant.
03 - Pour chicken broth into the pot and bring to a rolling boil. Reduce heat to medium-low and simmer for 20 minutes to develop flavors.
04 - Add shredded chicken and frozen peas to the simmering broth. Continue cooking for 5 minutes.
05 - In a mixing bowl, whisk together flour, baking powder, and salt. In a separate bowl, whisk melted butter, milk, and egg until combined. Pour wet ingredients into dry ingredients and stir until just combined without overmixing.
06 - Drop tablespoon-sized portions of dumpling batter onto the simmering soup surface. Cover the pot and cook for 18-20 minutes without lifting the lid until dumplings are puffed and cooked through.
07 - Remove and discard the bay leaf. Stir in fresh chopped parsley. Taste the soup and adjust seasoning with additional salt and pepper as needed.
08 - Ladle soup with dumplings into bowls and serve immediately while hot.