Sift the flour and cocoa powder into a bowl, make a well in the center, and add the beaten egg. Gradually beat in the flour mixture from the sides, then slowly beat in the milk until smooth. Cover with plastiv wrap and let stand for 30 minutes.
Arrange the apple on a foil-covered broiler rack. Springle with a little sugar, then cook under a preheated medium broiler for 3 minutes. Turn, sprinkle with the remaining sugar, and cook for 2 minutes. Transfer to a bowl, add the bananas, and mix well. Put the butter, lime rind, and juice into a seperate bowl, mix, and chill.
Heat a little oil in a skillet over high heat. Beat the batter and pour 4 tablespoonfuls into the skillet to make a layer. Cook until firm underneath, flip over, and cook the other side. Remove and keep warm. Rapeat with the remaining batter. Divide the filling between the pancakes, drizzle the melted chocolate over the filling, roll up, and serve with the lime butter.