Heat the olive oil to medium-high heat in a 12-inch cast-iron or nonstick skillet. Add the onions and saute until translucent, about 5 minutes. Add the potato slices, season with salt and cook over low and slow heat until the potatoes are softened and lightly golden brown around the edges, 30 to 40 minutes, gently shaking the pan from time to time to prevent the potato slices from sticking. When the potatoes are ready, reserve 2 tablespoons of the olive oil from the skillet (now infused with the flavor of those onions and potatoes) and drain the potatoes in a colander or on a paper towel.
Beat the eggs with a generous pinch of salt in a large bowl for about 1 minute. Add the drained caramelized potatoes and onions and stir with a fork to lightly break up the potatoes (this will give the finished Tortilla de Patata a wonderful light fluffy texture). Heat 1 to 2 tablespoons of the reserved olive oil in the same skillet until very hot. Pour in the egg and potato mixture and cook on one side, gently shaking the pan occasionally, until the underside is set and very lightly browned, about 5 minutes. Using a plate to cover the pan, carefully invert the omelet onto the plate and then gently slide the omelet back into the pan to cook on the other side until just set and light golden brown, about 5 minutes more. Do not overcook. This Tortilla de Patata is best when barely runny in the very center. Serve immediately with some slices of fresh baguette, or make ahead to serve later in the day at room temperature. Enjoy!