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Preheat the oven to 425°F (220°C). Line a large sheet pan with parchment paper. Drizzle a thin layer of olive oil over the parchment and spread it so the surface looks lightly glossy. This helps the bottom crisp and keeps the latkes from sticking.
Using the large holes of a box grater or a food processor, grate the potatoes and onion. You want long, even shreds, not a paste. If the mixture looks very watery already, move quickly to the next step so it does not darken too much.
Pile the grated potatoes and onion into a clean kitchen towel. Gather the corners, hold it over the sink, and twist firmly. Keep twisting until very little liquid drips out and the shreds feel light and almost dry. This step is key for a crisp, not stodgy, sheet.
Transfer the squeezed potatoes and onion to a large bowl. Add the eggs, kosher salt, black pepper, and potato starch (or cornstarch or flour). Mix well until every strand is coated and the mixture holds together when you press a handful. If it feels loose and wet, sprinkle in a bit more starch; if it feels too stiff, add a spoonful of beaten egg.
Scoop the mixture onto the prepared sheet pan and spread it out all the way to the edges. Aim for a thin, even layer, similar to a thick hash brown. Press down gently with your hands or a spatula so there are no tall mounds and everything makes good contact with the pan. Drizzle the remaining olive oil over the top in a thin zigzag.
Bake for 35–45 minutes, rotating the pan halfway through. The latkes are ready when the edges are deeply golden and very crisp, and the center looks set and lightly browned. If the edges darken too quickly while the center is still pale, move the pan to a higher rack.
Let the sheet rest for about 5 minutes so it firms up slightly. Use a sharp knife or pizza cutter to slice into squares or rectangles. Lift pieces with a spatula and serve hot with your favorite toppings, from sour cream and applesauce to labneh, salmon, or fried eggs.