Place peeled and chopped potatoes in the crockpot insert in a single layer as best you can.
Pour the chicken or vegetable broth over the potatoes. The broth should come about halfway up the potatoes; it helps cook and flavor them without making them soggy.
Dot the top with butter, then sprinkle with 1 teaspoon salt and 1/4 teaspoon black pepper.
Cover and cook on low for 3 to 4 hours, or on high for 1.5 to 2 hours, until the potatoes are very tender and easily pierced with a fork.
Turn off the crockpot and drain any excess liquid if there is a lot. Leave a little for moisture, though.
Add milk (or cream) and sour cream or cream cheese if using. Mash directly in the crockpot with a potato masher for a chunkier texture, or use a hand mixer for smoother potatoes. Stir until creamy and combined.
Taste and adjust seasoning with more salt and pepper if needed. If the potatoes are too thick, add a little more warm milk, 1 tablespoon at a time.
Serve warm, topped with chopped chives or parsley and an extra pat of butter if you like.