With a sharp small knife, cut the ends from each plantain and cut a lengthwise slit through the skin on 2 sides of the plantain. Peel the skin off and cut the plantains into 1-inch-thick chunks. In a 12-inch nonstick skillet, heat 1/2-inch oil over medium heat. The oil should sizzle when you toss the chunks in.
Fry the chunks in batches (avoid crowding) until golden, for approximately 2 minutes. Transfer the plantains with tongs to a plate lined with 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 each plantain chunk to a 1/4-inch thick disc (about 3 inches in diameter).
Turn the heat back on to medium and fry the flattened plantains in batches in the reserved oil until they're golden, approximately 3 minutes. Do not overcrowd. Transfer with tongs to a plate lined with paper towels to drain excess grease.