Heat the olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and sauté for about 5 minutes until translucent.
Stir in the minced garlic, diced carrots, and celery. Cook for an additional 5-7 minutes until the vegetables are tender.
Add the dried thyme, dried rosemary, salt, and black pepper to the pot, stirring to combine.
Pour in the chicken broth and bring the mixture to a simmer. Allow it to cook for 10 minutes.
Add the shredded chicken and frozen peas to the pot. Stir well and let it cook for another 5 minutes.
In a separate bowl, whisk together the heavy cream, all-purpose flour, and milk until smooth. Gradually add this mixture to the pot while stirring to thicken the soup.
Allow the soup to simmer for an additional 5-7 minutes, stirring occasionally until thickened to your desired consistency.
If using biscuit mix, prepare according to package instructions and drop spoonfuls onto the simmering soup. Cover the pot and cook for 10 minutes, until the biscuit topping is fluffy and cooked through.
Serve hot with a ladle and enjoy!