Beat egg yolks in a medium mixing bowl until light and lemon colored. Add mashed banana, butter, and milk, stirring mixture well.
Sift together flour and baking powder. Add to banana mixture, mixing well.
Beat egg whites (at room temperature) in a small mixing bowl until stiff, but not dry; fold into batter.
Drop batter by teaspoonfuls into deep, hot oil (375°). Fry until golden brown, turning once. Drain well on paper towels. Dredge in powdered sugar. Serve warm.