Halve the potatoes lengthwise and, with a sharp knife or, preferably, a mandoline, slice them crosswise about 1/16 inch thick. Toss the potatoes with 1/2 teaspoon of the salt and half of the pepper. In 9 inch castiron skillet, heat 1/4 cup of the olive oil over medium heat. Add the potatoes and cook, tossing occasionally with a spatula, until golden and crisp. Try to avoid clumping but, if they stick together a bit don't worry. Set the pan aside.

Heat 2 tablespoons of the olive oil in another skillet over medium low heat and saute the onions, stirring occasionally, for about 20 minutes, or until very soft and slightly golden.

Preheat the oven to 350 degrees. In a large bowl, beat the eggs together and stir in the remaining 1/4 teaspoon each of salt and pepper, and the onions. Remove the potatoes from the pan with a slotted spoon and let them drain for a moment in a colander. Wipe the potato cooking pan with a paper towel, then add the remaining 2 tablespoons oil to the skillet. Heat the skillet over low heat, stir the potatoes into the egg mixture, and immediately pour it into the hot skillet. Cook for about 8 minutes, or until the bottom of the cake is slightly golden. Place a large plate upside down on top of the skillet, invert it, and turn the cake onto the plate. Slide the cake back into the pan. Finish cooking in the oven for 4 to 5 more minutes, or until the eggs are set. Cool in the pan for 5 minutes, then cut into wedges or squares, depending on the number of people you want to serve. Serve warm or at room.

Variation: Add 2 roasted, peeled, and diced red peppers and 1 tablespoon of paprika to the onion mixture after it is cooked.