01 - In a large Dutch oven or heavy pot, heat butter and olive oil over medium heat. Add diced onion, sliced carrots, and sliced celery. Sauté for 5 to 6 minutes until vegetables are softened. Add minced garlic and cook for 1 additional minute until fragrant.
02 - Stir in the chicken pieces and season with salt, pepper, dried thyme, and dried parsley. Cook for approximately 4 minutes until the chicken is lightly browned on all sides. Sprinkle 2 tablespoons of flour over the mixture and stir well to coat evenly.
03 - Pour in the chicken broth and bring to a simmer. Reduce heat, cover the pot, and let cook for 15 minutes to allow flavors to meld.
04 - While the soup simmers, whisk together 1 1/2 cups of flour, baking powder, salt, and pepper in a mixing bowl. Stir in melted butter and milk until just combined, then gently fold in fresh parsley if using. Be careful not to overmix the dough.
05 - Return to the pot and stir in heavy cream and frozen peas. Using two spoons, drop dollops of dumpling dough, about 1 heaping tablespoon each, onto the surface of the simmering soup, spacing them evenly.
06 - Cover the pot tightly and simmer gently over low heat for 15 to 18 minutes without lifting the lid, until the dumplings are puffed and cooked through.
07 - Taste the broth and adjust seasonings as needed. Ladle into bowls and serve hot.