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Heat the oil in a medium skillet over high heat until it shimmers, about 3 minutes. Add the plantains and fry them until they turn golden on all sides, about 3 minutes. Use a slotted spoon to transfer them to a paper towel-lined plate to drain, then place between 2 sheets of parchment paper. Reduce the heat to medium.
Flatten the plantains by pressing down on them with a heavy-bottomed pan. Return 1/2 of the flattened plantains to the oil and re-fry until deep golden on both sides, about 4 to 6 minutes. Transfer back to the paper towel-lined plate to drain and repeat with the remaining flattened plantains. Sprinkle with salt and serve immediately.