Mom's Scalloped Potato Gratin

Preheat the oven to 400 degrees F (200 degrees C). Grease a 2-quart casserole dish with 2 tablespoons butter and set aside.

Peel potatoes and cut at a 45-degree angle into 1/4-inch thick round slices.

Arrange 1/3 of the potato slices in an even layer in the bottom of the prepared dish. Season the layer very generously with salt, and sparingly with the freshly ground black pepper, and cayenne, if using. Top evenly with 1/3 of the Cheddar cheese. Repeat this process two more times for a total of three layers of potatoes, except for the last third of the cheese. Slowly and carefully pour in the milk, without upsetting the layers. The milk should almost, but not quite, cover the potatoes.