Beat 5 eggs with an electric mixer until foamy, 2–3 min. Add 4 tablespoons hot water and continue beating until the mixture is very thick and pale, 3–5 min. Gradually sprinkle in 150 g sugar while beating until fully dissolved, 2–3 min.
In a separate bowl, sieve together 100 g flour, 50 g cocoa powder, and 0.5 teaspoon baking powder. Pour the sieved mixture onto the egg mixture and gently fold together using a spatula, lifting from the bottom to top, until just combined.
Line a baking sheet with parchment paper and spread the batter evenly on it. Bake in a preheated oven at 225 °C (437 °F) on the second rack from the bottom for 10–12 min, until the cake springs back when lightly touched.
Remove the cake from the oven and run a knife around the edges to loosen it. Lay a tea towel flat on a work surface, turn the cake out onto it, brush the parchment paper with cold water, and carefully peel it off. While still warm, roll the cake tightly with the tea towel and let it cool completely for 30 min.
Combine milk, sugar, eggs, and coconut flakes in a saucepan. Cook over medium heat, stirring constantly, for 8–10 min until thickened. Remove from heat, stir in rum and mashed bananas, and let cool to room temperature.
Whip the cream with powdered sugar and cream stiffener until stiff peaks form. Reserve a portion in a piping bag for decoration.
Unroll the cooled cake. Spread the coconut filling evenly over the cake. Spread the remaining whipped cream on top. Carefully roll up the cake again and transfer to a serving plate.
Pipe the reserved whipped cream on top for decoration and sprinkle with grated chocolate.
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