In a small nonstick skillet, melt 1 tablespoon of the butter. Add half of the potatoes and pat them into a disk about 1/2 inch thick. Cook over moderately high heat, turning once, until golden, 3 minutes per side. Transfer the potato galette to a baking sheet. Repeat with the remaining 1 tablespoon of butter and potatoes. Bake the galettes for 10 minutes, until cooked through and crisp; transfer to a platter and let stand for 15 minutes.