In a small bowl, mix sugars and cinnamon until blended. In a large bowl, whisk the first five beignet ingredients. In another bowl, whisk egg, bananas, milk and 2 tablespoons oil until blended. Add to flour mixture; stir just until moistened.
In an electric skillet or deep fryer, heat oil to 375°. Drop tablespoonfuls of batter, a few at a time, into hot oil. Fry about 45-60 seconds on each side or until golden brown. Drain on paper towels. Roll warm beignets in sugar mixture. Yield: about 3 dozen.