Wash, peel (optional), and cut the potatoes into roughly 1½–2 inch chunks so they cook evenly. Place the potato pieces into the crockpot.
Pour the chicken or vegetable broth over the potatoes, then add 1 teaspoon of salt and the black pepper. Dot the butter pieces over the top.
Cover and cook on LOW for 3–4 hours or on HIGH for 1½–2 hours, until the potatoes are fork-tender. Cooking time varies with crockpot model and potato size — test by piercing a piece with a fork.
When potatoes are tender, drain any excess liquid if there's a lot, but reserve a bit of cooking liquid if needed to loosen the mash. Return potatoes to the crockpot on the warm setting.
Warm the milk (in the microwave or stovetop) so it blends smoothly, then add it a little at a time while mashing. Mash with a potato masher for a rustic texture or use a hand mixer for ultra-smooth results. Stir in sour cream if using.
Adjust seasoning with more salt and pepper to taste. If the potatoes are too thick, stir in a splash of reserved cooking liquid or more warm milk until you reach your desired consistency.
Finish by stirring in a knob of butter for shine, then sprinkle chopped chives or parsley over the top before serving. Keep on the warm setting until ready to serve, stirring occasionally to prevent a skin from forming.