Heat about 1-inch of oil in heavy-bottomed saucepan over medium heat until a deep-fry thermometer inserted in the oil registers 340 degrees F. Line a large plate with paper towels.
Peel the plantains and discard the skins. Slice into 1/4-inch thick pieces. Fry the plantains in oil, turning occasionally, until a golden brown color, about 2 to 4 minutes. The longer the plantains fry the sweeter they are. Remove with a slotted spoon and drain on paper towels. Sprinkle the plantains with a little salt.
Put the sugar and cinnamon in a brown bag, drop the warm plantains into the bag, and shake to coat evenly. Serve with rum whipped cream or ice cream, if desired.
Whip the cream just until soft peaks form. Add the rum and whip again, taking care not to over whip your cream. Serve now or refrigerate until ready to serve.
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