Cut the chicken breasts into bite-size pieces.
Place all the ingredients EXCEPT the tortellini and milk/heavy cream into the base of the slow cooker and pour in 2 cups of hot water.
Set the slow cooker on low and cook for 8 hours. With 30 minutes left in the cooking cycle, take off the lid and shred the chicken into the soup. Then, add the tortellini into the soup. Let finish cooking until until tortellini are tender. Just before serving, swirl in the milk or heavy cream into the soup. Once finished cooking, ladle soup into serving bowls immediately to keep the pasta from overcooking.
If you are cooking this in the Instant Pot or Multi-Cooker, cook the base of the soup and then add the tortellini and cream and switch to warm or stovetop mode and let the tortellinis cook for about 10 minutes, allowing them to swell.
Note: if your slow cooker lets off a lot of liquid or "runs hot," then you might need to add 1-2 cups of water or chicken stock when you add the tortellini. They will soak up quite a bit of liquid. Also, be ready to serve this quickly so the pasta doesn't overcook on warm or stovetop mode.
Prepare the salad.
Serve Slow Cooker Chicken Tortellini Soup with Parmesan cheese garnish and salad.