Prepare the potatoes: Slice the potatoes into thin discs (about 1/4-inch thick). A mandoline slicer works beautifully for consistency. Keep the skin on for extra fiber or peel for a smoother result.
Cook the potatoes: Heat the olive oil in a non-stick or cast-iron skillet over medium-high heat. Once shimmering, add the potato slices in an even layer. Fry in batches for about 3-4 minutes per side, removing when tender and lightly golden. Drain on paper towels and sprinkle with salt.
Sauté the onions: With just a tablespoon of olive oil left in the pan, add the chopped onions. Cook for 2-3 minutes, stirring occasionally, until softened and slightly crispy.
Assemble the tortilla: Spread the onions evenly at the bottom of the skillet. Layer the fried potato slices in a scalloped pattern. Pour the beaten, salted eggs over the top. Gently shake the pan to ensure the eggs evenly distribute.
Cook and broil: Cook on medium until the edges of the tortilla begin to set (about 4-5 minutes). Transfer the skillet to a preheated broiler and cook for an additional 5 minutes or until the top is golden and set. Alternatively, flip the tortilla onto a plate and return it to the pan inverted for stovetop finishing.
Rest, slice, and serve: Allow the tortilla to cool for 5 minutes before slicing into wedges. Serve warm or at room temperature for the ultimate flavor.