Heat the olive oil in a large skillet over medium heat. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, until the vegetables are softened, about 5-7 minutes. Add the minced garlic and cook for another minute, until fragrant.
Transfer the sautéed vegetables to your slow cooker. Add the chicken broth, diced tomatoes (with their juice), Italian seasoning, salt, and pepper. Stir everything together to combine.
Cover the slow cooker and cook on low for 6-8 hours, or on high for 3-4 hours. The vegetables should be very tender.
About 30 minutes before the soup is done, stir in the cheese tortellini. Make sure they're submerged in the broth. Cover and continue cooking.
Once the tortellini are cooked through (they'll float to the top), add the fresh spinach and heavy cream. Stir gently until the spinach is wilted, which should only take a couple of minutes.
Ladle the soup into bowls. If desired, garnish with freshly grated Parmesan cheese and a sprinkle of fresh parsley. Serve hot with your favorite crusty bread or a side salad.