Prepare the bananas: Place granulated sugar in a shallow pie plate or baking dish. Toss bananas in sugar; shake off excess.

Place 4 spring roll wrappers on a work surface with 1 point facing you (so that they look like diamonds). Place 1 banana on each wrapper, 1 inch above bottom point. Carefully begin wrapping banana from the bottom up, keeping the roll as tight as possible. Fold in the sides of the wrapper (like a burrito). Brush 1 inch of top point with some of the beaten egg, and continue to wrap, pressing to secure roll. Repeat with remaining bananas, wrappers, and egg. Place rolls in a single layer on a sheet pan lined with a damp paper towel. Freeze 1 hour.

Heat oil to 325°F in a large Dutch oven. Fry banana rolls, 2 or 3 at a time, until golden brown, 6 to 7 minutes. Drain on paper towels.

Prepare the sauce: Cook brown sugar and butter in a skillet over medium-high, whisking constantly, until melted and bubbly, 3 to 4 minutes. Tilt pan away from you, and carefully add the rum, whisking until smooth. Remove pan from heat, and stir in cream and pepper.

Slice banana rolls in half diagonally. Spoon sauce over top, sprinkle with pecans, and serve with ice cream.