Heat a non-stick pan over medium heat and melt about 1 – 1/2 tbsp of butter. Add sliced banana and 1 tbsp sugar. Saute until golden. In a bowl combine the remaining sugar with cinnamon and set aside. In another bowl beat eggs with milk and set aside. Remove the bread crust, and flatten the slices with a rolling pin. Spread about 1-2 teaspoons of the banana mixture along one edge of the bread. Brush the other side with the prepared egg wash. Gently but tightly roll up the bread around the banana mixture and seal to make a roll. Continue with the remaining bread. Melt about 1 tbsp of butter in a pan. Coat the rolls in the egg mixture and place seam side down. Cook 3-4 rolls at a time. When browned, turn a quarter turn and continue until all sides are cooked and browned nicely. Clean the pan slightly with a paper towel and repeat until all rolls are cooked. Roll into the sugar-cinnamon mixture or dust with powdered sugar. Serve warm.