Sauté vegetables: In a large 5 to 6-quart Dutch oven or heavy soup pot, melt butter with olive oil over medium heat. Add diced onion, celery, and matchstick carrots. Sauté for 5 minutes until vegetables soften. Stir in minced garlic and cook for 1 minute until fragrant.

Form roux: Sprinkle flour over the softened vegetables. Cook, stirring constantly with a wooden spoon, for 1 to 2 minutes to cook out raw flour taste.

Whisk liquids & herbs: Slowly pour in chicken bone broth while whisking continuously to prevent lumps. Whisk in half-and-half (or heavy cream), dried thyme, Italian seasoning, salt, and black pepper. Bring to a gentle boil, then reduce heat to medium-low and simmer for 5 minutes until slightly thickened.

Cook gnocchi & chicken: Add uncooked potato gnocchi and shredded chicken into the simmering broth. Cook uncovered for 4-5 minutes until the gnocchi float to the surface, indicating they are pillowy and tender.

Wilt spinach & add cheese: Stir in fresh baby spinach and freshly grated Parmesan cheese. Simmer for 1-2 minutes until spinach is wilted and cheese is completely melted into the velvety broth. Remove from heat.

Ladle & serve: Ladle hot soup into wide shallow bowls. Top with freshly shaved parmesan cheese, coarse black pepper, and fresh thyme sprigs. Serve immediately with warm garlic breadsticks!