In a heavy pot, add enough oil to fill halfway. Heat until a deep-frying thermometer reads 350 degrees F or the handle of a wooden spoon begins to sizzle immediately when dipped in the oil.
Add the plantains and fry until bright yellow and slightly golden brown, about 4 minutes. Remove from the oil with a slotted spoon to a sheet of parchment paper. Make sure all pieces are standing tall on the cut side, then place another sheet over the top. Using a small plate, glass or other flat item smash each piece into a 1/4-inch jagged circle.
Place the plantain discs back in the oil and fry for 4 to 6 more minutes or until the edges are golden brown. Remove to a wire rack and sprinkle with salt.