Preheat your oven to 180°C (350°F) and line your baking tray with parchment paper.
In a large mixing bowl, use the electric mixer to whisk the eggs and granulated sugar together until the mixture thickens and becomes pale, about 5-7 minutes.
Sift the flour, baking powder, and salt into the egg mixture and gently fold in using a rubber spatula. Be careful not to deflate the batter.
Add the vanilla extract and mix until just combined.
Pour the batter into the prepared baking tray, spreading evenly. Bake in the preheated oven for 12-15 minutes or until the cake is golden and springs back when touched.
Once out of the oven, immediately turn the cake onto a clean kitchen towel dusted with powdered sugar. Carefully peel off the parchment paper and roll the cake up in the towel from one end. Let it cool completely.
Meanwhile, in a saucepan, combine the mashed bananas and caramel sauce over low heat. Stir until warmed through and slightly thickened, about 3-4 minutes. Remove from heat and let it cool.
In a separate bowl, whip the heavy cream and powdered sugar until soft peaks form.
Unroll the cooled sponge and spread the whipped cream over the surface. Spoon the banana caramel mixture evenly on top.
Carefully roll the cake back up without the towel, and place seam-side down on a serving platter.
Chill for at least 30 minutes before slicing for clean cuts.
Serve with additional banana slices and a drizzle of caramel sauce if desired.