Heat butter and olive oil in a large, heavy-bottomed pot over medium-high heat until foaming subsides. Sauté onion, carrots, and celery with ¼ tsp salt and ½ teaspoon pepper until softened and just starting to brown. Add garlic and cook for 1 minute, until fragrant.
Deglaze the pot with the wine, scraping any brown bits from the bottom with a wooden spoon. Simmer until almost all of the liquid is evaporated, 2-3 minutes. Stir in flour and cook for 1-2 minutes.
Gradually whisk in chicken stock and simmer to thicken slightly. Whisk in half and half, thyme, and Italian seasoning. Bring to a simmer (not a rolling boil), stirring or whisking.
Add gnocchi and simmer for 3-5 minutes until tender and cooked through (they'll start to float). Stir in parmesan, shredded chicken, and spinach leaves. Simmer for 2-3 minutes, until chicken is hot and spinach is wilted.
Season to taste with nutmeg (if using), salt, and pepper. The soup will thicken as it sits. For a thinner-textured soup, serve right away. For a thicker soup, let stand 5-10 mins, keeping the soup warm or gently reheating, if needed.
Serve, topped with additional freshly-grated Parmigiano Reggiano and cracked black pepper, with crusty Italian bread on the side for dipping.
