Preheat oven to 350°F (175°C). Line a jelly roll pan with parchment paper.
In a bowl, beat eggs and sugar until thick and pale.
Sift in flour, cocoa powder, baking powder, and salt. Fold gently until combined.
Add vanilla extract and mix. Pour batter into the prepared pan and spread evenly.
Bake for 10-12 minutes. While baking, place a clean kitchen towel on the counter and dust with powdered sugar.
Once baked, flip the cake onto the towel, peel off parchment, and roll up gently from the short side. Cool completely.
Whip heavy cream with powdered sugar and vanilla extract until stiff peaks form.
Unroll the cake, spread the whipped cream over it, and place banana slices evenly.
Re-roll the cake tightly, drizzle with melted chocolate, and garnish if desired.
Chill for at least 1 hour before serving.