In a large pot or Dutch oven over medium heat, cook the sausage, breaking it up with a spoon, until browned and cooked through. If the sausage is very lean, add the olive oil as needed.

Add the onion, garlic, carrots, and celery. Cook for 4 to 5 minutes, stirring occasionally, until the vegetables begin to soften.

Stir in the chicken broth, potatoes, Italian seasoning, salt, and black pepper. Bring the soup to a boil, then reduce the heat to a simmer.

Cover and simmer for 15 to 20 minutes, or until the potatoes are tender.

Stir in the heavy cream, spinach, and Parmesan cheese. Cook for 2 to 3 minutes more, just until the spinach is wilted and the soup is creamy.

Taste and adjust seasoning with more salt and pepper if needed. Serve warm.