Heat 1 tablespoon olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add 1 pound Italian sausage and cook, breaking it up with a wooden spoon, for 5-7 minutes until browned and crumbled.
Add the finely chopped onion, diced carrots, and diced celery to the pot. Cook, stirring occasionally, for 5-6 minutes until the vegetables begin to soften. Stir in the minced garlic and cook for 1 minute until fragrant.
Pour in 6 cups chicken broth and the entire can of undrained diced tomatoes. Add 1 teaspoon Italian seasoning, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Bring the soup to a boil, then reduce heat to maintain a gentle simmer. Cook for 10 minutes to allow the flavors to meld.
Add the entire package of refrigerated cheese tortellini to the simmering soup. Cook according to package directions, usually 5-7 minutes, stirring occasionally, until the tortellini are tender and floating.
Stir in 3 cups chopped fresh spinach and cook for 1-2 minutes until wilted. Turn off the heat and stir in 1/2 cup heavy cream and 1/2 cup grated Parmesan cheese until fully incorporated and the soup appears creamy. Serve immediately with additional Parmesan cheese for topping.