Preheat oven to 375°F (190°C) and line your jelly roll pan with parchment paper. Lightly grease it and prepare a sugared kitchen towel for rolling.
Beat eggs and sugar until thick and pale. Add mashed bananas and vanilla extract.
Whisk flour, baking powder, baking soda, and salt in a separate bowl. Gently fold into the banana mixture.
Pour batter into the pan and spread evenly. Bake for 12–15 minutes until springy.
Immediately flip onto the sugared towel, peel off parchment, and roll up with the towel inside. Cool 45 minutes.
Beat cream cheese, powdered sugar, and vanilla until smooth. Fold in whipped cream.
Unroll cooled cake, spread filling evenly, and roll up again (without towel). Wrap and chill 2 hours before slicing.