Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the diced onion and cook until translucent, about 3-4 minutes.
Stir in the minced garlic, sliced carrots, and chopped celery. Cook for an additional 5 minutes, stirring occasionally.
Add the chicken pieces to the pot and cook until they are no longer pink, about 5 minutes.
Stir in the dried thyme, rosemary, salt, and black pepper.
Pour in the chicken broth and bring the mixture to a boil then turn to medium low heat.
Let the stew simmer for about 15 minutes, or until the vegetables are tender and the chicken is cooked through.
Add the frozen peas and stir into stew.
Drop the thawed dumpling dough over the simmering stew, spacing them out a bit.
Cover the pot with a lid and let the dumplings steam for about 15 minutes. Avoid lifting the lid during this time to ensure proper cooking.
Once the dumplings are cooked through and fluffy, gently stir the stew to mix in the dumplings.
Garnish with fresh parsley if desired and serve hot.