Plain old mashed potatoes are always brilliant, and it's hard to imagine a Thanksgiving table without them. Still, every once in a while we like to change things up. But not too much. Here, a small amount of Parmesan cheese adds earthiness and nuttiness to the classic smooth, creamy potatoes, and turns a traditional side into something inspired with no extra work.
Just be sure to go easy on the salt, and taste at the end. Parmesan adds a bit of saltiness to this dish.
Also, when you add the milk mixture to the crushed potatoes and stir, you will think, "Wait! That's too much liquid!" Don't worry. As the potatoes cook and sit they will thicken up. If you make them ahead of time you can reheat them gently over low heat, adding some more hot milk as necessary and stirring frequently.
You have several options for mashing the potatoes. You can use an old-fashioned potato masher, which will probably yield some lumps (which some of us like). You also can use a potato ricer, which looks kind of like an oversized garlic press. You put the potatoes in, press them through the fine-holed disc at the bottom, and the potatoes come out a bit like grains of rice, though they quickly turn into creamy mashed potatoes when you mix them with the remaining ingredients.
There also is a food mill, which works similarly, only you crank the potatoes through the holes on the bottom disc with a handle. This tool also is good for pureeing things like cooked tomatoes or berries, as it strains out the seeds and skins, only allowing the smooth fruit mixture to pass through.