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Rinse the leeks well, discard the green part, then cut them into rings 1/2 inch thick. Place the pieces in a bowl of cold water and let them soak for 30 minutes, then drain and rinse carefully under cold running water.
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Heat 3 Tablespoons of the olive oil in a pan. When it is warm, add the leeks, season with salt and pepper and saute for about 30 minutes, until soft. Transfer the leeks to a bowl and allow them to cook for 1 hour.
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In a large bowl, lightly beat eggs with a pinch of salt. Add the cooked leeks and mix thoroughly.
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Place a large omelet pan over medium heat with the remaining tablespoon of olive oil. When the oil is hot, add the leek-egg mixture. When eggs are well set and the frittata is well detached from the bottom of the pan, put a place, face down, over the pan. Holding the plate firmly, reverse the pan and turn the frittata out.
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Return the pan to the flame. Carefully slide the frittata onto the pan to cook the other side. After 2 minutes, reverse the frittata onto a service dish.