In a 6-8 quart slow cooker, combine carrots, broccoli, onion, garlic, broth, milk, and cashews.
In a small bowl, toss together salt, pepper and paprika.
Sprinkle seasoning mixture into the crock pot.
Cut butter into cubes and place in slow cooker. Give ingredients a few stirs, cover, and set on Low for 4-6 hours. (The broccoli does not need much longer than this to fully cook! If you want to set it on High, be sure to check it occasionally so the ingredients do not burn.)
Once all vegetables are completely tender, use an immersion blender to puree the soup.
(If you do not have an immersion blender you can also use any other high speed blender and puree the soup in batches. Be careful, however, because the soup will be very hot!!)
Lastly, stir in cheese just before serving.
Serve soup with your favorite piece of gluten-free toast and enjoy!