Preheat the oven to 350°F (175°C). Line a 15x10 inch baking sheet with parchment paper, allowing the paper to hang over the edges for easy removal.
In a mixing bowl, beat the eggs and granulated sugar together until thick and pale, about 5 minutes. Add 1 teaspoon of vanilla extract and mix well.
In another bowl, combine cocoa powder, baking powder, salt, and flour. Gradually fold the dry mixture into the egg mixture until just combined.
Gently fold in the mashed bananas until evenly incorporated.
Pour the batter into the prepared baking sheet, spreading it evenly. Bake for 12-15 minutes or until the cake springs back when lightly touched.
Remove the cake from the oven and let it cool in the pan for 5 minutes. Carefully invert the cake onto a clean kitchen towel dusted with powdered sugar. Peel off the parchment paper and roll the cake tightly with the towel starting from one short end. Let it cool completely.
While the cake is cooling, whip the heavy cream in a mixing bowl until it begins to thicken. Gradually add the powdered sugar and ½ teaspoon of vanilla extract, and continue whipping until stiff peaks form.
Once the cake is completely cool, carefully unroll it. Spread the whipped cream filling evenly over the surface, leaving a small border around the edges. Roll the cake up tightly again, this time without the towel.
Place the rolled cake seam-side down on a serving platter. If desired, garnish with chocolate chips on top. Cover with plastic wrap and chill for at least 30 minutes before slicing.
To serve, slice the roll into 1-inch pieces and enjoy!