Place the potatoes, broth, garlic and butter into a 6qt slow cooker. Season with salt; mix together and cover with lid. Cook on HIGH setting for 4 hours or LOW setting for 7-8 hours, until very tender.
Mash potatoes with a potato masher or electric beater. Stir the sour cream and milk through until well combined and creamy (add more milk if desired). Stir through the parmesan cheese.
Keep on low or warm setting until ready to serve.
Notes
*You can use unpeeled potatoes if you like skin in your mash! Slow cooker mashed potatoes maintain a creamy consistency for a couple of hours after mashing if the lid stays on the slow cooker. If the lid has been removed and the potatoes have dried out a little, just add a little more milk to reach desired consistency.