With cut sides of garlic clove, firmly rub the bottom and sides of a 1 ½-quart baking dish. Then generously coat bottom and sides with butter.
In a pitcher, whisk together cream and milk. (A 4-cup glass measuring pitcher works great for this.)
Layer ⅓ of potato slices into prepared baking dish. Season generously with salt and pepper and pour over ⅓ of the cream mixture. Repeat with 2 remaining layers, finishing with cream mixture that should just cover the potatoes.
Bake 70 minutes, until bubbly on the edges and golden brown on top (see recipe note #2). Sprinkle with cheese if using and bake 10 minutes more. Let stand 10 to 15 minutes. Garnish with chives and serve.
A mandoline or food processor slicing disc makes quick work of this.
To protect against spills, place the baking dish on a parchment lined, rimmed baking sheet before placing in the oven. If gratin is getting too brown, cover lightly with foil.
You can skip the cheese in this gratin. Or, if you prefer a cheesy gratin, add an additional 4 ounces, for 6 ounces total. Sprinkle the first 2 layers of raw, seasoned potato slices with 2 ounces each before baking. Then add the final 2 ounces to melt during the last 10 minutes of baking.