Preheat the oven to 250 degrees. Preheat a Belgian or standard waffle iron on medium-high heat.
Grate the potatoes in a food processor fitted with the grating disk. (You can also grate them by hand on a box grater as you would grate carrots.) Transfer the potatoes to a clean kitchen towel and spread them out. Working quickly, roll the towel up like a jelly roll. Press firmly to squeeze out any moisture but not so hard that you break up the potatoes. Transfer the potatoes to a large mixing bowl. Grate the onion the same way you grated the potatoes, spreading it out on the kitchen towel and squeezing out the moisture. Add the onion to the bowl. Add the butter, egg, flour, 1½ teaspoons salt, and ½ teaspoon pepper and mix with a fork.
When the waffle iron is hot, brush both sides generously with melted butter. Place a generous ¹⁄₃ cup of the potato mixture on each of the four waffle divisions, spreading it out with a fork. Cook for 5 to 10 minutes, depending on your waffle iron, until the potatoes are browned and crispy. Transfer the potatoes, browner side up, to a sheet pan lined with parchment paper and keep warm in the oven for up to 30 minutes while you prepare the next batch. Repeat with the remaining mixture to make 8 hash browns. Transfer to a platter, sprinkle with salt, and serve hot.
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