Preheat the oil in a deep-fryer or large cast-iron skillet to 375 degrees F (190 degrees C).
Peel bananas, and slice them in half lengthwise, then crosswise into fourths. Place one piece of banana diagonally across the corner of a spring roll wrapper, and sprinkle with brown sugar to taste. Roll from the corner to the center, then fold top and bottom corners in, and continue rolling. Dip your finger in water and brush the last edge to seal. Repeat with remaining banana pieces.
Fry a few banana rolls at a time in the hot oil until evenly browned. Remove to paper towels to drain. Serve hot or cold.