In a large pot, heat olive oil over medium heat. Add Italian sausage and cook, breaking it up with a spoon, until browned and cooked through. Remove excess fat if necessary.
Add diced onion, garlic, carrots, and butternut squash to the pot. Sauté for 5 minutes until vegetables begin to soften.
Pour in chicken broth and add dried thyme. Bring to a boil, then reduce heat and simmer for 15 minutes, or until vegetables are tender.
Add cheese tortellini to the soup and cook according to package instructions, usually 5-7 minutes, until tortellini are tender.
Stir in baby spinach and cook for 1-2 minutes until wilted. Season with salt and pepper to taste.
Ladle soup into bowls and top with grated Parmesan cheese before serving.