Preheat your oven to 180°C (350°F). Line the baking sheet with parchment paper, ensuring there are no wrinkles.
In a mixing bowl, whisk the eggs and granulated sugar together using an electric mixer until the mixture is thick, pale, and forms ribbons (about 5 minutes).
Gently fold in the plain flour, baking powder, and salt using a rubber spatula, being careful not to deflate the mixture.
Once the batter is combined, pour it onto the prepared baking sheet and spread it evenly with the spatula.
Bake in the preheated oven for 12-15 minutes, or until the cake springs back when touched and is lightly golden.
While the cake is baking, prepare a clean kitchen towel by dusting it with powdered sugar. Once the cake is done, remove it from the oven and quickly invert it onto the prepared towel. Peel off the parchment paper and roll the cake up carefully with the towel. Let it cool completely in this rolled shape.
In a small saucepan over low heat, combine the mashed bananas, caramel sauce, heavy cream, and vanilla extract. Stir gently until warmed and evenly mixed.
Once the cake has cooled, unroll it carefully. Spread the banana and caramel mixture evenly over the surface of the cake.
Roll the cake back up without the towel, starting from one end. Place the seam side down on a serving dish.
To serve, slice the roulade with a serrated knife. Optionally, dust with powdered sugar before serving.