Heat olive oil in a large Dutch oven or soup pot over medium-high heat. Add the Italian sausage, breaking it up with a spoon, and cook until browned and crumbled, about 5-7 minutes. Drain any excess grease, leaving about 1 tablespoon in the pot.

Add the diced onion, carrots, and celery to the pot. Cook, stirring occasionally, until the vegetables begin to soften, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Pour in the chicken broth and add the undrained diced tomatoes, dried oregano, dried basil, salt, and black pepper. Bring the mixture to a simmer, then reduce the heat to medium-low, cover, and let it gently simmer for 10-15 minutes to allow the flavors to meld.

Increase the heat to medium and add the gnocchi to the simmering soup. Cook according to package directions, typically 2-3 minutes, until the gnocchi are tender and float to the surface. Do not overcook.

Stir in the fresh spinach and cook just until it wilts, about 1-2 minutes. Remove the pot from the heat and stir in the heavy cream (or half-and-half) and grated Parmesan cheese until well combined and creamy.

Taste and adjust seasoning if needed. Ladle the soup into bowls, garnish with fresh chopped parsley and additional grated Parmesan cheese if desired. Serve hot.