Heat oil in a large cast iron or other ovenproof skillet over medium heat. Add potatoes, onion, and salt. Use a heatproof spatula to coat potatoes with oil. When oil begins to bubble, reduce heat to medium-low and cook, turning frequently, until potatoes are tender but not browned, 20–25 minutes.

Using a slotted spoon, transfer potatoes and onion to a large heatproof bowl. Add eggs and stir gently to combine; do not break up potatoes. Drain and wipe out skillet.

Heat 3 Tbsp. oil in skillet over medium-high heat. Add egg-potato mixture and cook, stirring constantly but gently to keep potatoes intact, until eggs begin to set (eggs will look scrambled), about 2 minutes. Spread mixture in an even layer; reduce heat to medium-low. Preheat broiler to high.

Cook tortilla, shaking pan occasionally to prevent it from sticking, until eggs are nearly cooked through, about 12 minutes. Transfer skillet to oven and broil until eggs are set and top of tortilla is browned, about 2 minutes.

Remove from oven. Invert a large plate over skillet. Using oven mitts (skillet and potatoes will be very hot; use caution), hold plate firmly over skillet and flip, releasing tortilla onto plate. Let sit at room temperature for at least 20 minutes before serving.