In a large pot, heat olive oil over medium heat. Add the diced onion, minced garlic, carrots, and celery. Cook until softened (about 5–7 minutes).
Stir in the shredded chicken along with low-sodium chicken broth, frozen peas, dried thyme, and rosemary. Bring to a gentle simmer.
In a small bowl, whisk together the flour and heavy cream until smooth.
Gradually add the cream mixture to the pot while stirring constantly to avoid lumps.
Allow the soup to simmer for an additional 10–15 minutes until it thickens up nicely. Season with salt and pepper to taste.
Ladle the soup into bowls and garnish with freshly chopped parsley.