Heat the olive oil in a large pot or Dutch oven over medium-high heat and add the onions, carrots, and celery. Cook for 5-6 minutes, stirring occasionally, or until the vegetables begin to soften.
Stir in the minced garlic and Calabrian chilies if using and cook for about 30 seconds, or until fragrant.
Add the butter and sprinkle the flour over the vegetables and stir well. Cook for 1-2 minutes, stirring constantly, to remove the raw flour taste.
Add the chicken, spices, chicken stock, and half and half.
Bring the soup to a gentle boil, then reduce the heat to medium-low and simmer for 15-17 minutes, or until the carrots and celery are tender and the broth has slightly thickened. Once the chicken is cooked, remove it from the pot and shred it using two forks or dice it.
Add the gnocchi and cooked chicken to the pot. Cook for 3-4 minutes, or until the gnocchi are tender and begin to float to the surface.
Reduce the heat to low and stir in the Parmesan cheese and spinach. Cook for another 2-3 minutes, stirring occasionally, until the spinach wilts and the cheese melts into the broth.
Season with salt and black pepper. Serve immediately with extra Parmesan cheese on top, if desired and enjoy!