Peel the potatoes. If they are large, slice them in half. In a large pot, cover them with cool water and boil until they are just fork-tender. Avoid overcooking or the potatoes will not slice nicely.
Thinly slice the cooked potatoes. Using a mandolin slicer produces uniform slices, but it's not essential. A sharp knife will work too.
Heat half of the oil in an ovenproof skillet over medium heat and sauté the onions, just until translucent but not browned. Remove them to a small bowl.
Whisk the eggs in a large mixing bowl. Add the sliced, cooked potatoes, sea salt, and sautéd onions.
Add the remaining oil to the frying pan and when hot, pour in the egg-potato-onion mixture. Let it cook for a minute or two, just until the edges are set.
Transfer the skillet to the oven and bake at 350 F. for 20 minutes or until the egg has set. A toothpick inserted in the center should come out clean.
Run a spatula around the edge of the skillet to loosen the tortilla. Invert a serving plate over the skillet and flip the plate and the pan over together. The tortilla will release easily.
Allow to cool slightly. Slice into wedges or small squares and serve warm or at room temperature.