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1
Make the latke mixture: Combine the grated potatoes and grated onion in a large, clean tea towel. Bundle up, hold over the sink or a garbage can, and squeeeeeeeze into oblivion, to get rid of all that extra moisture. (Just when you think it's done, do a couple more squeezes.) Dump into a large bowl. Add 1 egg, 3 tablespoons flour, and the 1 teaspoon salt. Mix to combine.
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2
Set up the dredging stations: Add the remaining flour to one shallow bowl and season with a pinch of salt. Add the remaining egg to another shallow bowl, season with a pinch of salt, and whisk with a fork until smooth.
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3
Add the vegetable oil to a large cast-iron skillet-adjusting the quantity to yield a roughly 1/2-inch thickness. Set over medium-high heat on the stove.
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4
Meanwhile, dredge the chicken: Dredge one chicken breast half in the flour, then the egg, then coat with 1/2 cup latke mixture (so, about 1/4 cup on each side). Use your hands to really seal the latke mixture all around (disposable latex gloves come in handy here). Some of the coating might try to slip off-no big deal, just make sure the chicken is completely covered before it goes in the pan. Repeat with the remaining chicken breast halves.
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5
Cook two pieces at a time. You don't want to overcrowd the pan, which would lead to steaming. Cook for 4 to 5 minutes on the first side, until deeply golden brown on the bottom. Flip, then cook for another 4 minutes or so, until the other side is browned and the meat is cooked through. Transfer to a paper towel-lined plate to drain any excess oil. Repeat with the remaining chicken breast halves.
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6
Psst: You can heat the oven to its lowest temperature to keep the first batch of latke chicken warm while frying the second batch. Or, if you're not eating immediately, you can keep all the chicken in there while you set the table or finish the other dishes-just not so long that it overcooks.
