Combine 1 cup of the flour, the baking powder, baking soda and salt in a large bowl. Gradually blend in water, beating with a whisk until smooth. Peel bananas, making a total of dozen pieces. Cut each banana in 3 pieces, crosswise. Coat bananas lightly with remaining cup of flour. Heat oil in wok over medium-high heat, until it reaches 375 degrees. Dip bananas in flour-water mixture, coating completely. Cook 4 to 6 pieces at a time in the oil, until golden, 3 to 5 minutes. Drain on absorbent paper. Serve hot with ice cream.