Wash and peel the potatoes. Cut them into bite-sized pieces.
Add the potatoes to a 6-quart slow cooker insert.
Melt one stick of butter in a large, glass measuring cup. Add the chicken broth and salt to the melted butter.
Pour the liquid over the potatoes and mix to combine.
Cover the slow cooker and cook on high power for 3-4 hours, or on low power for 7-8 hours.
Potatoes are done when they are pierced easily with a fork.
Pour in one cup of half and half. Use a potato masher to mash the potatoes until smooth. Trust the process! When you add the half and half it will look like too much liquid. But as you mash the potatoes, it will absorb.
Dot the top of the finished mashed potatoes with more butter, if desired.
Keep the potatoes warm in the slow cooker until ready to serve.