Preheat oven to 425°F Using 3 tablespoons of the butter, grease a heavy 8-inch skillet. Select a well-seasoned cast-iron skillet or one that has a heat-resistant handle. If the handle is not heat-resistant, cover with aluminum foil.
Using a floating-blade vegetable peeler, peel potatoes. With a large French chef's knife or a mandolin, cut potatoes crosswise into thin slices. You should have about 5 cups slices potatoes. Put potatoes into a large bowl and toss gently with salt and pepper.
Arrange one-third of the potato slices in a circular fashion around bottom and up the side of the skillet. Select slices that are uniform in size and shape. Dot with about 1/3 of the remaining butter and repeat layering two more times.
Place skillet over a medium-high heat and cook 4 minutes to brown the bottom of the potatoes. Remove from heat and cover potatoes with non-stick aluminum foil. Place a 9-inch Pyrex baking dish or pie plate on top of foil and press down firmly to pack potatoes together.
Place skillet and baking dish on rack in center of oven. You may want to place a sheet of aluminum foil on rack under skillet to catch any drippings that may run over. Bake 30 minutes. Remove Pyrex baking dish and foil and bake 5 minutes longer.
Remove skillet from oven and let stand for 5 minutes. Using a small metal spatula, gently loosen potatoes from side and bottom of skillet. Invert onto serving platter to unmold potatoes. Remove skillet and serve.