Heat the olive oil in a large pot or Dutch oven over medium heat. Add the diced onion and sauté until it becomes translucent, about 3-4 minutes.
Add the minced garlic, diced carrots, and diced celery to the pot. Cook for another 5 minutes, stirring occasionally, until the vegetables soften.
Stir in the shredded chicken and chicken broth. Bring the mixture to a simmer.
Add the frozen mixed vegetables, dried thyme, dried parsley, salt, and black pepper. Continue simmering for another 10-15 minutes, until the vegetables are heated through and tender.
Reduce the heat to low and stir in the heavy cream. Cook for an additional 5 minutes, allowing the soup to thicken slightly.
If you're using biscuit dough, prepare it according to the package or recipe instructions, and place spoonfuls of dough on top of the soup. Cover and cook for an additional 10-12 minutes until the biscuit topping is cooked through.
Taste and adjust seasonings if necessary before serving.
Serve the soup hot, garnished with fresh herbs if desired.