In a large pot, heat the olive oil over medium heat.

Add the chopped onion, carrots, and celery, and sauté for about 5 minutes until softened.

Stir in the minced garlic, thyme, rosemary, salt, and pepper, cooking for an additional minute.

Pour in the chicken broth and bring to a simmer.

Add the shredded chicken and frozen peas, then reduce the heat to low to keep warm.

In a separate bowl, combine the flour, baking powder, and salt.

Stir in the melted butter and milk until just combined. The batter will be thick.

Drop spoonfuls of the dumpling batter into the simmering broth.

Cover the pot and let the dumplings cook for about 15 minutes without lifting the lid.

Serve hot, garnished with fresh parsley if desired.