Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the onion, carrots, and celery. Cook until the vegetables soften, about 5 to 7 minutes.
Stir in the minced garlic, thyme, and rosemary. 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. Bring the mixture to a simmer.
Add the shredded chicken and the potato gnocchi to the pot. Cook according to the gnocchi package directions, usually until they float to the surface, about 3 to 5 minutes.
Reduce the heat to low. Stir in the heavy cream and Parmesan cheese until the cheese melts and the soup is heated through. Do not boil after adding the cream.
Season with salt and pepper to your preference.
Ladle the soup into bowls and garnish with fresh parsley before serving.
Notes
You can use store-bought rotisserie chicken to save time.
If you prefer a thicker soup, let it simmer uncovered for a few extra minutes before adding the cream.
Frozen gnocchi works well in this recipe; add them directly from the freezer.