Sauté the aromatics: In a slow cooker with sauté function (or a skillet), heat olive oil over medium. Add onion and cook for 3-4 minutes until soft. Add garlic and cook for 30 seconds until fragrant.
Add vegetables and seasonings: Place carrots, celery, and Italian seasoning in the slow cooker. Stir to combine.
Pour in broth and tomatoes: Add chicken broth and diced tomatoes. Stir well.
Cook on low: Cover and cook on low for 6-8 hours or high for 3-4 hours, until vegetables are tender.
Add tortellini and greens: 20-30 minutes before serving, stir in refrigerated tortellini and spinach. (For frozen tortellini, add 30-40 minutes before.)
Stir in cream and cheese: Add heavy cream and Parmesan (if using). Cook for 5-10 minutes until heated through. Season with salt and pepper.
Serve warm: Ladle into bowls and garnish with extra Parmesan or fresh herbs.