Scrub and peel potatoes and cut into 1-inch chunks.
Place potatoes, chicken broth, and 1 tablespoon butter into a 6-quart slow cooker. Cover and cook until tender about 3 – 4 hours on high heat or 6-7 hours on low. Stir twice while cooking. (It is okay if the potatoes brown slightly in a few spots.)
For garlic (if using), preheat oven to 400 Degrees F. Cut top ¼ inch off garlic head exposing the cloves, and place in a sheet of foil. Drizzle with olive oil and season with a little salt and pepper. Wrap foil around garlic head and roast for 40 - 50 minutes or cloves are soft and golden. Set aside to cool. Squeeze out the garlic cloves and set aside.
When potatoes can easily be pierced with a fork, remove lid and break up the potatoes in the slow cooker using a potato masher. Add roasted garlic cloves, remaining butter, sour cream, and ½ cup warm milk and mash until fairly smooth. If potatoes need to be thinned out, add more warm milk and season to taste with additional salt and pepper. Garnish with chives and serve warm.
Notes
Turn slow cooker to warm until ready to serve. You can make ahead and reheat on the stove or in the oven at 325 degrees F for 20 minutes.