Heat the oven to 400°F, with a rack in the top third. Using a mandoline or sharp knife, slice the potatoes as thin as possible, about 1?16 inch. Do not rinse or cover with water—the potatoes’ starch helps keep the galette intact.
Set the pan on a burner over medium-high heat. When the potatoes start to sizzle, let cook for another minute or two, then transfer the pan to the oven. Bake, uncovered, for 20 minutes, or until beautifully browned. To serve, invert the galette onto a cutting board and carefully cut into quarters; alternatively, invert directly onto a serving platter, leaving in one piece.