Arrange potatoes in a medium skillet (you should have enough to make a layer three potatoes deep over the bottom). Add oil and cook potatoes until soft on inside and crispy and browning on outside. Season with salt.
In bowl, whisk eggs with a small amount of water. Pour eggs over potatoes, lifting them so eggs mix. Cook over medium-low heat until omelet sets and is brown on bottom. Flip and cook until the second side is browned.
Serve, cut into wedges.