Peel and chop the russet potatoes, and chop the onion. Add the chopped potatoes and onion to your slow cooker along with the chicken stock, butter, minced garlic, salt, and ground black pepper. Give it a gentle stir so the ingredients are evenly distributed.
Cover the slow cooker and cook the soup mixture on low for 4 to 6 hours, or on high for 3 to 4 hours, until the potatoes are very soft and easy to mash. I like to check the potatoes at the earliest suggested time—they should be fork tender and almost falling apart. Stir occasionally if you can.
While the soup is nearing the end of its cooking time, prepare the thickening mixture. About 30 to 60 minutes before the soup is done, whisk together the heavy whipping cream, sour cream, and xanthan gum in a small mixing bowl until totally smooth and thick. This will help the soup achieve a creamy, luscious texture.
Stir the thickened cream mixture (from Step 3) into the slow cooker with the potato soup. Switch the slow cooker to high (if it isn’t already), and cook for an additional 20 to 30 minutes so the soup thickens slightly and becomes extra creamy. Stir occasionally to ensure even distribution. For a silkier finish, I sometimes use an immersion blender for just a few pulses to partially blend the soup, but this is optional.