Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper, making sure the paper hangs over the edges for easy removal later.
In a mixing bowl, beat the eggs and granulated sugar together using an electric mixer until the mixture is thick and pale, about 5 minutes. Add 1 teaspoon of vanilla and mix until fully combined.
In another bowl, whisk together the flour, cocoa powder, baking powder, and salt. Gently fold the dry ingredients into the egg mixture until just combined.
Pour the batter onto the prepared baking sheet and spread it evenly. Bake for 12 to 15 minutes, or until the cake springs back when touched.
Once baked, remove the cake from the oven and immediately turn it out onto a clean kitchen towel dusted with powdered sugar. Carefully peel off the parchment paper.
Starting at one end, roll the cake up tightly using the towel to help, and let it cool completely in this position.
While the cake cools, whip the heavy cream with 2 tablespoons of powdered sugar and ½ teaspoon of vanilla extract until stiff peaks form.
Unroll the cooled cake carefully and spread the mashed bananas evenly over the surface, followed by a layer of whipped cream. Sprinkle the chocolate chips on top.
Roll the cake back up without the towel, wrap it in plastic wrap, and refrigerate for at least 30 minutes to set.
When ready to serve, slice the roll into pieces with a sharp knife and enjoy.