In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for 3-4 minutes until softened.
Stir in the minced garlic, diced carrots, and celery. Cook for another 4-5 minutes until the vegetables begin to soften.
Add the chicken pieces to the pot, seasoning them with thyme, rosemary, and black pepper. Cook for about 5-7 minutes until the chicken is browned on all sides.
Pour in the chicken broth and add the diced potatoes. Bring the mixture to a gentle boil, then reduce the heat and let it simmer for 15-20 minutes until the potatoes are tender.
In a small bowl, mix the flour with a few tablespoons of the soup broth to create a slurry. Stir this mixture back into the soup to thicken it.
Slowly pour in the heavy cream, stirring continuously to combine. Allow the soup to simmer for an additional 5 minutes until it thickens further.
Stir in the frozen peas, and let the soup cook for another 3 minutes. Adjust the seasoning with salt to taste.
Serve hot, garnished with fresh parsley for a pop of color and flavor.