Preheat oven to 375°F (190°C). Line a jelly roll pan with parchment paper and lightly grease it.
In a medium bowl, whisk together flour, baking powder, cinnamon, baking soda, and salt.
In a large bowl, beat eggs and granulated sugar until thick and pale. Beat in vanilla and mashed bananas.
Gradually add the flour mixture to the banana mixture, stirring just until incorporated.
Spread batter evenly in the prepared pan. Bake for 12-15 minutes, or until the cake springs back when touched.
Immediately loosen the edges of the cake and turn it out onto a clean kitchen towel dusted with powdered sugar. Roll the cake up with the towel from the short end and let cool completely.
To make the filling, beat cream cheese, brown sugar, and vanilla extract until smooth. Fold in whipped topping.
Carefully unroll the cake. Spread the filling evenly over the cake and reroll without the towel. Chill in the refrigerator before serving.
Dust with powdered sugar and drizzle with caramel topping before serving.