With a sharp small knife cut ends from each plantain and cut a lengthwise slit through skin. Cut plantains crosswise into 1-inch-thick pieces and, beginning at slit, pry skin from pieces. In a 12-inch nonstick skillet heat 1/2-inch oil over moderate heat until just hot enough to sizzle when a plantain piece is added. Fry plantains in batches, without crowding, until tender and just golden, 2 to 3 minutes on each side. With tongs transfer plantains as fried to paper towels to drain.
Remove skillet from heat and reserve oil. With the bottom of a heavy saucepan or a wide solid metal spatula flatten plantains to 1/4-inch thick (about 3 inches in diameter). Into a bowl of warm salted water dip flattened plantains, 1 at a time, and drain them well on paper towels.
Heat reserved oil over moderate heat until hot but not smoking and fry flattened plantains in batches, without crowding, until golden, about 3 minutes. With tongs transfer tostones as fried to paper towels to drain and season with salt if desired.
Serve tostones immediately.