Cut off the ends of the plantains. Using a knife, score each plantain lengthwise in 3 places and use your thumb to pry off the peel. Slice the plantains crosswise 1 inch thick.
In a saucepan, heat 2 inches of oil to 350°. Working in batches, fry the plantains just until pale golden, 4 minutes. Using a slotted spoon, transfer the plantains to a paper towel–lined baking sheet. Using a meat pounder, flatten the plantain slices to a 1/2-inch thickness.
Heat the oil to 375°. Working in batches, fry the plantains until crisp and golden, about 4 minutes. Drain on paper towels and sprinkle with salt. Serve right away.