In a large skillet, heat oil over moderate heat to 350 degrees.
With a sharp knife, cut the ends of each plantain. Run the knife down two opposite sides and score. Then using your hands, peel away the skin.
Cut the plantains at an angle into 1 ½-inch thick slices.
In batches, fry the plantain pieces until golden brown on each side, about 2 minutes per side. Transfer to a paper towel to drain.
Place the plantain on a flat surface and press down on it firmly with the bottom of a mug of skillet until flattened to ¼ inch.
Reheat the oil and fry the tostones again until they reach a deeper golden brown, about 1-2 minutes on each side.
Drain on a paper towel. Sprinkle with sea salt while still hot and serve warm.