Cut the peeled plantains into lengths of 2-1/2 inches. Heat the oil – which should be at least 1-1/2 inches deep in the pan – and add a few of the plantain pieces. Be careful not to crowd the pan. Fry over medium heat, turning them over from time to time until they are an even golden brown, about 10 minutes.
Remove and drain. Place a piece of the plastic on each of the plates of a tortilla press. Put one length of the fried plantain upright on the bottom plate and smash it down with your hand to flatten slightly. Close the press and flatten the plantain out, turning the plastic around (because the plates are not always even) until you have an almost transparent even disk about 5 inches across. The edge will not be perfectly even, but don’t worry.
Peel back the top plastic and sprinkle the plantain with salt. Carefully transfer to the hot oil. Fry on both sides until crisp and a deep golden brown. Drain on brown paper and serve immediately.
*It is very important, when choosing the plantains, that while the skins are still green the flesh inside is just beginning to ripen and has a sweet flavor. The totally green ones are more starchy and bland.