In a large soup pot, heat the olive oil over medium heat.
Add the diced onion and cook until translucent, about 5 minutes.
Stir in the minced garlic, carrots, and celery. Cook for an additional 5 minutes, until the vegetables soften.
Add the dried thyme and rosemary, stirring to combine.
Pour in the turkey broth and bring the mixture to a boil.
Once boiling, reduce the heat to a simmer and add the shredded turkey.
Simmer for about 15 minutes, allowing the flavors to meld.
Stir in the heavy cream and frozen peas, then heat through for another 5 minutes.
Season with salt and pepper to taste.
If you prefer a smoother texture, use a blender or immersion blender to purée some of the soup, then return it to the pot.
Serve hot, garnished with fresh parsley.