Trim both ends off the plantains and cut them crosswise in 2-inch-long pieces.
Peel off the skin.
(There should be 3 pieces per plantain.
)
In a small heavy saucepan, pour oil to a depth of about 2 inches and heat until the surface shimmers.
Fry 2 to 3 pieces of plantain at a time, turning with the aid of two wooden spoons, until golden brown on all sides, about 6 minutes.
Drain on paper towels.
Repeat until all are fried and drained.
Reserve pan of oil off heat.
Preheat the oven to 200°.
Put 1 piece of plastic on the bottom of the tortilla press and stand 1 plantain piece upright in the center of the plastic.
Flatten the plantain slightly with the palm of your hand.
Place the second piece of plastic on top of the plantain.
Close the hinged top and press the handle gradually to flatten the plantain to a circular shape with irregular edges about 5 inches in diameter.
Pour about 4 tablespoons of oil from the pan of reserved oil into a large nonstick skillet and heat until the oil shimmers.
Peel the top piece of plastic from the tostone.
Sprinkle with salt.
Flip the tostone onto your palm and carefully remove the second piece of plastic.
Carefully transfer the tostone to the hot oil and fry, turning with a wide spatula, until brown on both sides.
Drain on paper towels.
Keep warm on a paper-lined baking sheet in the oven.
Repeat the process with the other plantains until all are fried.
Serve warm.