Preheat your oven to 350°F (175°C). Line a 15x10-inch jelly roll pan with parchment paper and lightly grease it.
In a large mixing bowl, whisk together the mashed bananas, eggs, sugar, vegetable oil, and vanilla extract until smooth and well combined.
In a separate bowl, sift together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, folding gently until just combined. Do not overmix.
Pour the batter into the prepared pan and spread evenly. Bake for 12-15 minutes until the cake springs back lightly and a toothpick comes out clean.
Immediately invert the cake onto a clean kitchen towel dusted with powdered sugar. Peel off the parchment paper and roll the cake with the towel inside. Let cool completely in rolled shape.
Whip the cream until stiff peaks form. If desired, fold in the chopped walnuts.
Unroll the cooled cake and spread the whipped cream evenly over the surface, leaving a small border around the edges.
Roll the cake back up without the towel. Place seam side down on a serving plate and drizzle generously with caramel sauce. Optionally sprinkle walnuts on top.
Refrigerate the cake roll for at least 30 minutes before slicing. Serve chilled or at room temperature.