First, make sure the potatoes are the size of golf balls or smaller. You may have to chop some of the larger ones up. Try to ensure all the pieces are of equal size.
Next, in the bottom of a 5-quart minimum slow cooker, add the potatoes, garlic cloves, and chicken broth. Stir very well.
Dice half of the butter, and scatter it across the top.
Replace the lid on the slow cooker, and turn to HIGH. Cook for 3-4 hours.
When the potatoes are done (easily pierced with a knife), turn off the slow cooker.
Add the rest of the butter and warm milk, and mash with a potato masher or hand mixer. Once the potatoes are as lumpy (or lump-free) as you like, add salt and pepper, to taste.
Serve in a bowl garnished with fresh chives.