Adapted from Smitten Kitchen
1/2 cup finely grated aged Pecorino Romano (or parm, or gruyere - basically any grateable cheese)
1 tablespoon cornstarch
1/2 teaspoon fine sea salt
1/2 teaspoon ground black pepper
3 tablespoons unsalted butter, melted, or olive oil
2 pounds potatoes, peeled, cut into 1/8-inch-thick, ideally on a mandolin
Heat your oven to 375°F. Combine the cheese, potato starch or cornstarch, salt, and pepper in a small dish. Taste a pinch; you want it to have a strong salty-peppery kick, because it’s going to be distributed throughout the dish.
Pour 1 tablespoon butter or oil into the bottom of a 9-inch-diameter cast-iron or ovenproof skillet (it's OK if your skillet is a little bigger - either increase the potatoes or just know that your galette will be a touch thinner), and swirl it up the sides.
Arrange the potatoes in overlapping concentric circles in a single layer at the bottom of the pan. (This will use approximately a quarter of your sliced potatoes.) Drizzle with 1 teaspoon butter or oil, and sprinkle with 2 tablespoons of the cheese-pepper mixture. You’ll need to repeat this three or four times to use up your potatoes (depending on their size). At the end, you should have about 1 tablespoon cheese-pepper mixture left over; reserve this. Drizzle any remaining melted butter over the top.
Lightly coat a piece of foil with nonstick spray and cover the skillet tightly with it. Put in heated oven for 35 minutes, at which point the potatoes will be almost tender. With a towel, use your hands to press firmly on the foil to compact the potatoes a bit.
Remove and reserve the foil, sprinkle the remaining cheese mixture on top, and bake for 25 to 30 minutes more, until lightly brown all over. Press again with the foil, remove, then briefly run under the broiler (5 mins or so) for an even golden-brown finish.
Once the galette is out of the oven, let it rest in the skillet for a few minutes before running a knife around to ensure that it is loose. Gently tip the skillet over your sink to drain any excess butter or oil. Invert it onto a plate or cutting board, then flip right side up. Serve warm or at room temp.