Make the cake: Place the peeled bananas in a medium bowl and use a fork to mash them. Add the eggs, vanilla, and sugar and whisk until the mixture turns pale yellow.
Add the flour, baking powder, baking soda, and salt and whisk to combine.
Grease a baking sheet well and line with parchment paper.
Pour the batter onto the baking sheet and use a spatula to spread evenly.
Bake for 12 minutes, or until the bread is golden brown and springs back when gently pressed.
Cover a large, clean dish towel with powdered sugar (this will help keep the cake from sticking to the towel). While the cake is still warm, carefully flip the baking sheet onto the towel. Lift up the sheet and remove the parchment paper.
Starting from a short end, gently roll up the cake with the towel. Let cool for at least 1 hour.
Make the filling: Add the cream cheese to a medium bowl and whip with a fork until light and fluffy. Add the sugar, vanilla, and milk. Mix until the filling is silky and smooth.
Add the melted chocolate and fold with a spatula to combine.
Unroll the banana bread and spread the filling evenly over it. Roll the banana bread back up without the towel, wrap the outside with the towel or plastic wrap, and chill for 4 hours.
Remove the roll from the fridge and sift powdered sugar over the top. Top with whipped cream. Run a vegetable peeler across a chocolate bar to sprinkle chocolate curls over the whipped cream.