Cut off the ends of the plantains and then carefully cut a slit down the length of the skin without cutting into the plantain itself. Using a wooden spoon, pry up the edges of the peel and pull off the skin. Once the peel is removed cut the plantain crosswise into 3 or 4 pieces, each about 2 to 3 inches long.
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.