Preheat your oven to 350°F (175°C). Line the jelly roll pan with parchment paper and lightly grease it.
In a large mixing bowl, beat the eggs and granulated sugar together using an electric mixer on high speed until pale and fluffy, about 5 minutes. Add in the vanilla extract and mix to combine.
In another bowl, sift together the flour, cocoa powder, baking powder, and salt. Gradually fold this dry mixture into the egg mixture using a rubber spatula until just combined, being careful not to overmix.
Gently fold in the mashed bananas until evenly distributed through the batter.
Pour the batter into the prepared jelly roll pan and spread it evenly. Bake for about 10-12 minutes or until a toothpick inserted in the center comes out clean.
Once done, remove from the oven and let it cool in the pan for a few minutes. Then, transfer the cake to a cooling rack and let it cool completely.
While the cake is cooling, whip the heavy cream with powdered sugar until stiff peaks form. Fold in the mini chocolate chips.
Once the cake is completely cool, carefully remove it from the pan and peel off the parchment paper. Spread the whipped cream mixture evenly over the cake.
Starting from one end, gently roll the cake up tightly to form a log shape. Use the parchment paper to help guide the roll. Wrap the roll in plastic wrap and refrigerate for at least 1 hour to firm up.
Before serving, unwrap the roll and dust with additional powdered sugar if desired. Garnish with banana slices and chocolate shavings, then slice and serve.