Add chicken broth and beer. Cover and cook on LOW for 4 to 5 hours or on HIGH for 3 to 4 hours.
Transfer half of mixture to a blender and blend until smooth. Process the remaining mixture until smooth and add it all back to crockpot. If desired, you can leave some of the potatoes as is so that there are a few chunks.
Stir in cheddar cheese until melted. Stir in cream. Let soup heat through for about 5 minutes.