Step 1: Prepare the Sponge Cake

1. Preheat the oven to 350°F (175°C). Line a 10×15-inch baking sheet with parchment paper and lightly grease it.
2. Beat the eggs and sugar in a large bowl until the mixture becomes pale, thick, and triples in volume (about 4-5 minutes).
3. Gently fold in vanilla, flour, baking powder, and salt, being careful not to deflate the batter.
4. Add the melted butter and fold gently until fully incorporated.
5. Pour the batter onto the prepared pan, spreading it evenly. Bake for 10-12 minutes until golden and springy to the touch.
6. Transfer the cake onto a clean kitchen towel dusted with powdered sugar. Roll it up gently with the towel and let it cool. This prevents cracks when rolling later.

Step 2: Make the Chocolate Filling

1. Heat the heavy cream in a saucepan until it begins to simmer.
2. Remove from heat and pour over the chopped chocolate. Let it sit for 1 minute, then stir until smooth.
3. Add butter for extra silkiness, then let the ganache cool until thickened but still spreadable.

Step 3: Assemble the Roll

1. Unroll the cooled sponge cake and spread a generous layer of chocolate ganache over the surface.
2. Place banana slices evenly across the filling, ensuring a balanced distribution.
3. Carefully roll the cake back up, using the parchment paper to guide it. Wrap in plastic wrap and chill for 30 minutes to set.

Step 4: Make the Chocolate Drizzle

1. Heat heavy cream and pour over the chocolate chips. Stir until smooth and glossy.
2. Drizzle over the chilled cake roll, letting it cascade down the sides.
3. Garnish with banana slices and shaved chocolate for an extra touch of elegance.