My grandmother made this every single week for 40 years. When I finally asked her why she never stopped she just smiled and handed me the empty pot to scrape.

My grandmother made these three-ingredient scalloped potatoes in a black slow cooker every single Sunday for as long as I can remember. She learned the bones of the recipe in the Depression, when stretching a sack of potatoes and a bit of dairy had to feed a whole family. Years later, when I finally asked why she never stopped making them, she just smiled and handed me the empty pot to scrape, the sides still coated with that creamy, browned sauce. This is a plain, honest dish: thin rounds of potatoes, a simple milk-based sauce, and a little butter, left to bubble away until everything is tender and golden at the edges. It’s the kind of recipe you make when money is tight, time is short, or you just want something that tastes like home.

These slow cooker scalloped potatoes are hearty enough to sit at the center of a simple meal with just a green salad or some cooked frozen peas alongside. In true Midwestern fashion, they’re wonderful next to baked ham, meatloaf, roast chicken, or a skillet of sausage. If you’re keeping it humble and thrifty, serve them with fried eggs and sliced tomatoes for supper. A little black pepper on top at the table is all they really need, but a spoonful of tangy applesauce or pickled beets on the side brings out their old-fashioned comfort.

Servings: 6

3 pounds russet or Yukon Gold potatoes, peeled and sliced very thin (about 1/8 inch)

Lightly grease the inside of a 4- to 6-quart slow cooker with a bit of the butter so the potatoes don’t stick and the edges can brown nicely.

Peel the potatoes, then slice them into very thin rounds, about 1/8 inch thick. The thinner you slice, the more tender and creamy the finished dish will be. A sharp knife works just fine; no need for anything fancy.

Layer a single, even layer of potato slices over the bottom of the greased slow cooker, overlapping them slightly like shingles so there are no big gaps.

Dot a small handful of the butter pieces over the potatoes, scattering them as evenly as you can. Pour just enough milk over this layer to barely moisten it; you don’t need to cover the potatoes completely yet.

Repeat the layering: potatoes, a few dots of butter, then a splash of milk, building up gentle, even layers until you’ve used all the potatoes. Reserve just enough milk to pour over the top at the end. The potatoes will settle as they cook, so don’t worry if the slow cooker looks fairly full.

Pour the remaining milk slowly over the top, tilting the slow cooker insert slightly if needed so the milk seeps down into the layers. You want to see milk creeping around the sides and just peeking up between some of the top slices, but not drowning them.

Place the lid on the slow cooker. Cook on HIGH for about 3 to 4 hours or on LOW for about 6 to 7 hours, until the potatoes are very tender when pierced with a fork and the milk has thickened into a creamy sauce. Avoid lifting the lid during the first 2 hours so the heat stays steady.

For a slightly browned, more set top layer, leave the lid slightly askew for the last 30 to 45 minutes of cooking to let a bit of steam escape. You should see the edges bubbling and some golden color forming on the uppermost potato slices.

Once the potatoes are fully tender and the edges are golden and bubbly, turn off the slow cooker. Let the scalloped potatoes rest, covered, for 15 to 20 minutes. This short rest lets the sauce thicken up and makes it easier to scoop out neat servings.

Serve the potatoes hot, scraping every bit of the creamy sauce from the sides of the slow cooker. Just like my grandmother did, don’t be surprised if the pot is nearly licked clean before you can even think about leftovers.

If you have a little more to spare than they did in the Depression years, you can dress this up without losing its spirit. A teaspoon or so of salt and a good grinding of black pepper over each potato layer will deepen the flavor. If you keep a small onion on hand, you can finely slice or mince it and tuck a little between the potato layers for sweetness. A handful of shredded cheese on the very top during the last 30 minutes of cooking gives a browned, slightly crusty lid, though it does take it out of strict Depression-era territory. For a richer version, replace 1 cup of the milk with evaporated milk or a splash of cream. If you need to make it ahead, you can slice the potatoes and keep them covered in cold water in the refrigerator for up to 4 hours to prevent browning; drain and pat dry before layering so the sauce doesn’t get watery. For food safety, keep the slow cooker on HIGH if your model runs cool or is very full, so the milk comes up to a safe temperature quickly. Don’t leave the finished potatoes on the WARM setting for more than 2 hours; after that, cool leftovers promptly and refrigerate in a shallow container. Reheat thoroughly until steaming hot before serving again. Always discard any portion that has sat out at room temperature for more than 2 hours. If you’re cooking for someone who is very salt-sensitive, use unsalted butter and let everyone season their own serving at the table.