Preheat the oven to 400 degrees F.

Line a sturdy baking sheet with foil or place two flimsy baking sheets together. Should the gratin boil over, it will hit the baking sheet and not your oven. You want the pan sitting on a stable base, which is why you should double your baking sheets if they’re flimsy.

Peel potatoes and then slice them reasonably thinly. I prefer slicing them lengthways. If necessary, trim a flat “face” on each potato so they rest safely on the cutting board. Place potato slices in a large pot as you go.

When all the potatoes are sliced, pour just enough half-and-half or cream to cover. This will be 2 to 2 1/2 cups. Turn burner to medium high. Bring pot to a boil. Add the salt and pepper. Stir.

Cook until potatoes are nearly done. This will take about 20 minutes.

Meanwhile, peel and slice the squash in coins. Set aside.

Prepare the gratin dish: in a large shallow baking dish–about 11-12 inches around–run the halved garlic clove. You can either remove it or leave it in, according to your preference.

Generously butter bottom and sides of gratin dish.

Test potatoes: they should break easily with a spoon. Once they do, use a slotted spoon to arrange them in layers in the gratin dish, alternating with the squash. You will have more potato than squash.

Carefully ladle or pour the hot dairy over the potato/squash mixture. It may not come all the up to the top. That’s okay.

Place on baking sheet. Slide carefully into oven. Bake 20-30 minutes. Gratin is done with the top is bubbling, browned, and delicious-smelling.

Top with parsley, if you wish.

Note: Some cooks prefer white pepper, as black leaves visible dots. I don’t mind the black pepper.

You could toss in a handful of panko during the last 10 minutes of baking, if you have any. This is a lazy person’s way of topping with breadcrumbs. But it works.

Gratin keeps well, refrigerated, up to three days, assuming you can keep your hands off it.