Heat the olive oil in a large stockpot or Dutch oven over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic, diced carrots, and celery. Cook for an additional 5 minutes until the vegetables begin to soften.
Add the dried thyme and rosemary, stirring to combine.
Pour in the chicken broth and bring the mixture to a boil.
Once boiling, reduce the heat to a simmer. Add the shredded chicken and frozen peas, cooking for another 10 minutes.
In a separate bowl, whisk together the heavy cream, flour, and milk until smooth. Slowly pour this mixture into the soup, stirring continuously to avoid lumps.
Allow the soup to simmer for an additional 5-10 minutes until it thickens. Season with salt and pepper to taste.
If using biscuit mix, prepare the biscuits according to package instructions and bake them while the soup thickens.
Serve the soup hot, optionally topped with warm biscuits.