Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, carrots, and celery. Cook until softened, about 5 to 7 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir constantly for 1 minute to cook out the raw flour taste.
Gradually whisk in the chicken broth until smooth. Add the thyme and rosemary. Bring the mixture to a simmer.
Reduce the heat to low, cover, and let it simmer for 10 minutes to allow the vegetables to soften and the broth to thicken slightly.
Stir in the shredded cooked chicken and the gnocchi. Cook according to the gnocchi package directions, usually about 3 to 5 minutes, until the gnocchi float to the top.
Remove the pot from the heat. Stir in the heavy cream and Parmesan cheese until fully combined and the soup is creamy. Do not boil after adding the cream.
Season with salt and pepper to your taste.
Ladle the soup into bowls and garnish with fresh parsley before serving.
Notes
You can use pre-cooked rotisserie chicken to save time.
If you prefer a thicker soup, allow it to simmer uncovered for a few extra minutes before adding the cream.
Shelf-stable gnocchi works well, but frozen gnocchi may require slightly longer cooking time.
For a garlic parmesan flavor boost, add 1/4 teaspoon of garlic powder with the flour.