Preheat the oven to 350 degrees F. Rub the garlic all over the inside of a 3-quart baking dish, then mince it. Grease the dish with about 1/2 tablespoon butter.
Slice the potatoes about 1/8 inch thick (a mandoline works well). Combine in a large saucepan with the minced garlic, the remaining 2 1/2 tablespoons butter, the half-and-half, creme fraiche, flour, thyme, mace, 2 1/2 teaspoons salt, and pepper to taste. Bring to a boil over medium-high heat and cook, stirring, until the mixture thickens slightly, 1 to 2 minutes. Stir in the chives and transfer the mixture to the prepared baking dish, shaking it to distribute the potatoes evenly. Bake, uncovered, until the potatoes are fork-tender, about 1 hour 5 minutes, occasionally spooning some of the liquid over the top. Let cool 10 minutes before serving.
You can also make the scalloped potatoes in individual ramekins; bake about 40 minutes.