In a large pot, heat olive oil over medium heat. Add diced onion, carrots, and celery. Sauté for about 5 minutes, until the vegetables are softened.
Stir in minced garlic, thyme, rosemary, salt, and black pepper. Cook for an additional 1-2 minutes until fragrant.
Pour in the chicken broth and bring the mixture to a boil.
Once boiling, reduce the heat to a simmer and add the shredded chicken and frozen peas.
While the soup simmers, open the can of biscuit dough and cut each biscuit into quarters.
Drop the biscuit pieces into the simmering soup, making sure they are evenly distributed.
Cover the pot and let the dumplings cook for about 10-12 minutes, or until they are fluffy and cooked through.
Stir in the heavy cream and let the soup heat through for another 2-3 minutes.
Serve hot, garnished with fresh parsley.