Prep the potatoes: Peel and cut the potatoes into even chunks about 1 1/2 inches wide. This helps them cook at the same rate and mash smoothly.

Load the slow cooker: Add the potatoes, broth, butter, 1 1/2 teaspoons salt, and pepper to the slow cooker. If you’re using garlic, add it now.

Cook low and slow: Cover and cook on Low for 4–5 hours or on High for 2 1/2–3 hours, until the potatoes are very tender when pierced with a fork.

Warm the dairy: Gently warm the milk (or half-and-half) on the stovetop or in the microwave. Warm dairy blends more easily and keeps the potatoes from tightening up.

Mash right in the pot: Turn the slow cooker to Warm. Use a potato masher to crush the potatoes and incorporate the butter and broth. For extra-smooth potatoes, switch to a hand mixer on low, but avoid overmixing.

Add the creaminess: Stir in the warm milk and sour cream. Start with 3/4 cup milk, then add more until the texture is creamy but not loose. Taste and adjust salt and pepper.

Finish and serve: Top with a few extra pats of butter, and sprinkle with chives if you like. Serve straight from the slow cooker or transfer to a warm bowl.

Keep warm (optional): You can hold the potatoes on Warm for up to 2 hours. Stir occasionally and add a splash of warm milk if they thicken.