In a large soup pot, heat the oil over medium-high heat. Add the onions, celery, carrots, and sauté for 5 minutes or until the onions are translucent.
Simmer:
Stir in the seasonings, broth, and turkey meat, and bring the soup to a boil before reducing the heat and simmering for an additional 20 minutes.
Once the veggies are tender, combine the cornstarch and water. Add the mixture to the soup along with the cream and green peas. Simmer for an additional 10 minutes or until the soup is thickened.
Serve:
Ladle the soup into bowls and top with chopped parsley if using.