Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper, allowing some overhang for easy removal later.
In a mixing bowl, beat the eggs and granulated sugar together using a hand mixer on high speed until thick and pale (about 5 minutes). Stir in the vanilla extract.
In another bowl, sift together the flour, baking powder, and salt. Gently fold the dry ingredients into the egg mixture using a rubber spatula, being careful not to deflate the batter.
Spread the batter evenly on the prepared baking sheet. Bake in the preheated oven for 20-25 minutes or until the cake is lightly golden and springs back when touched.
While the cake is baking, prepare a clean kitchen towel by sprinkling it with powdered sugar. Once the cake is done, immediately turn it out onto the prepared towel, peeling off the parchment paper.
While the cake is still warm, carefully roll it up in the towel, starting from the short side. Let it cool completely, seam side down.
Meanwhile, whip the heavy cream and powdered sugar together in a mixing bowl until stiff peaks form.
Once the cake has cooled, unroll it gently. Spread a layer of the whipped cream on top, followed by the mashed bananas and drizzle with caramel sauce.
Roll the cake back up, this time without the towel, and wrap it in plastic wrap. Refrigerate for at least 1 hour before serving.
Before serving, slice the roulade into portions and drizzle with additional caramel sauce if desired. Garnish with banana slices if you wish.