Heat 2 tablespoons of olive oil in your large pot or Dutch oven over medium heat. Add the diced onion, sliced carrots, and celery. Cook, stirring occasionally, until the vegetables are softened and the onion turns translucent—about 5 to 7 minutes. Stir in the minced garlic and cook for another minute until fragrant.
Add the cubed chicken breast to the pot and cook until lightly browned on all sides, about 4 minutes. Pour in the 4 cups of chicken broth, then add the dried thyme, rosemary, bay leaf, salt, and pepper. Stir everything together, bring the mixture to a gentle boil, then reduce the heat to low and let it simmer for 15 minutes to allow the flavors to meld.
While the broth simmers, whisk together 1 cup of all-purpose flour, 1 tablespoon of baking powder, and 1/2 teaspoon of salt in a mixing bowl. Add 1 cup of milk and stir just until combined. Be careful not to overmix—the dough should be slightly sticky but hold together.
Remove the bay leaf from the soup. Using a spoon or your fingers, drop spoonfuls of the dumpling dough onto the simmering broth. Cover the pot with a lid and let the dumplings cook for about 15 minutes without lifting the lid. This steam cooking is essential to ensure your dumplings turn out light and fluffy.
Once the dumplings are cooked through, gently stir in the frozen peas and chopped parsley. Cook for an additional 2-3 minutes until the peas are heated through. Taste and adjust salt and pepper as needed.