Slice potatoes and place in a large colander, sprinkle with 2 tsp. salt, and toss to coat. Let stand for 10 minutes. Pat dry with paper towels.
Heat oil in a large nonstick skillet over medium-high heat. Add potatoes and cook, turning occasionally, until crisp-tender, 10–15 minutes.
Add onion to potatoes in skillet; cook until onion and potatoes are soft, 5–8 minutes. Using a slotted spoon, transfer mixture to a large bowl; let cool slightly. Strain oil into a heatproof bowl; set aside.
Add eggs to potato mixture; season with salt. Wipe out skillet. Heat ¼ cup reserved oil over medium-high heat (chill remaining oil for another use). Add egg mixture, arranging potatoes to submerge.
Reduce the heat to medium-low and cook until the edges are set and the bottom is golden, adjusting the heat to prevent burning. Carefully invert onto a large plate, then slide back into the skillet, browned side up. Continue cooking until the center is set and reaches 160°F (71°C). Cut into wedges and serve warm or let cool briefly before serving.