Sauté the Veggies: In a large pot, heat olive oil over medium heat. Add onion, celery, and garlic, and cook until softened (about 5 minutes).
Add Carrots and Chicken: Add the shredded carrots and cooked chicken to the pot, stirring well.
Add Broth and Seasonings: Pour in the chicken broth, thyme, and Italian seasoning, and bring to a gentle boil.
Add Gnocchi: Reduce heat, add gnocchi, and let cook for 3-4 minutes until the gnocchi floats to the top and is tender.
Add Cream and Spinach: Stir in half-and-half (or cream) and spinach. Allow soup to simmer for another 3-5 minutes, until spinach wilts and soup is warmed through.
Season and Serve: Taste and adjust with salt and pepper as needed. Serve hot with crusty bread or salad on the side.