In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced chicken and cook until browned, about 5-7 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the chopped onion, garlic, carrots, and celery. Sauté for about 5-6 minutes until the vegetables are softened.
Stir in the flour and cook for another minute to form a paste, ensuring the flour is well combined with the vegetables.
Gradually pour in the chicken broth while whisking to avoid lumps. Bring the mixture to a simmer.
Add the heavy cream, thyme, rosemary, salt, and pepper. Stir until well combined.
Return the cooked chicken to the pot and add the frozen peas. Simmer for an additional 10-15 minutes, stirring occasionally, until the soup thickens slightly.
If using, bake the pie crust pieces in a separate oven according to package instructions until golden brown. Once done, you can break them into small pieces for topping.
Taste and adjust seasonings if needed. Serve hot, garnished with the pie crust pieces if desired.