Grease the slow cooker: Lightly grease the inside of a 4- to 6-quart slow cooker with a little butter or nonstick spray to help prevent sticking and make cleanup easier.
Make the brown sugar glaze: In a medium bowl, whisk together the melted butter and brown sugar until you have a thick, glossy mixture. It should look like a loose caramel sauce. If there are a few sugar lumps, keep stirring until they break up.
Combine potatoes and glaze: Add the dried potatoes to the slow cooker. Pour the brown sugar–butter mixture over the potatoes, scraping the bowl so you get every bit. Use a spatula or large spoon to gently toss the potatoes in the slow cooker until they’re evenly coated in the glaze.
Slow cook: Cover the slow cooker with the lid. Cook on HIGH for 3 to 4 hours, or on LOW for 5 to 6 hours, until the potatoes are very tender when pierced with a fork. About halfway through the cooking time, gently stir the potatoes to re-coat them in the glaze and keep the sugar from settling on the bottom.
Thicken and caramelize the glaze: Once the potatoes are tender, remove the lid and carefully stir again to coat them in the thickened glaze. Prop the lid slightly ajar with a wooden spoon or folded towel and continue cooking on HIGH for 20 to 30 minutes. This helps some moisture escape so the glaze reduces and clings to the potatoes, forming that shiny, sticky coating with lightly caramelized edges.
Finish and serve: Turn the slow cooker to WARM. Gently stir the potatoes one last time right before serving to coat them in the syrupy glaze. Serve straight from the slow cooker or transfer to a warm serving bowl, spooning extra glaze over the top. If you’d like, finish with a tiny sprinkle of salt at the table to balance the sweetness.
For a less sweet version, reduce the brown sugar to 3/4 cup and add a pinch of salt to the glaze before cooking. If you prefer a salted-caramel vibe, stir 1/2 teaspoon of kosher salt into the brown sugar and butter mixture. For a hint of spice that still works for picky eaters, add 1/2 teaspoon ground cinnamon or pumpkin pie spice to the glaze; it makes the potatoes taste a bit like candied yams.
You can also finish the cooked potatoes with a teaspoon of vanilla extract stirred into the glaze right at the end (off the heat) for a warm, cozy flavor. If your family likes a little texture, sprinkle toasted chopped pecans or walnuts over the potatoes just before serving, keeping a nut-free portion separate for anyone with allergies. For a richer sauce, whisk in 2 to 3 tablespoons of heavy cream to the glaze after cooking, then let it bubble on HIGH for another 5 to 10 minutes with the lid slightly open to re-thicken.
To make this dairy-free, use a dairy-free butter substitute that’s labeled for baking and cooking; avoid margarine spreads that are very watery, as they can thin the glaze too much.
Food safety tips: Keep the potatoes refrigerated within 2 hours of serving; store leftovers in a shallow container so they cool quickly. Reheat thoroughly until steaming hot before eating, either in the microwave or back in the slow cooker on HIGH. Do not leave the slow cooker on WARM for more than 4 hours once the potatoes are done. Always start with clean, well-rinsed potatoes and a clean slow cooker to avoid any contamination.