Preheat your oven to 350°F (175°C).
Grease a 9-inch round cake pan with oil or cooking spray. Optionally, line the bottom with parchment paper.
In a large mixing bowl, mash the very ripe bananas until smooth. Add granulated sugar, brown sugar, applesauce, water, and white vinegar. Whisk until well combined and smooth.
In another bowl, whisk together the all-purpose flour, unsweetened baking cocoa, baking soda, and salt until no lumps remain.
Gradually add the dry ingredient mixture to the wet ingredients, stirring gently with a rubber spatula until just combined. Do not overmix.
Fold in 1/2 cup of the semi-sweet chocolate chips until evenly distributed.
Pour the batter into the prepared cake pan and spread evenly. Sprinkle the remaining 1/3 cup chocolate chips on top.
Bake for 30-35 minutes or until a toothpick inserted in the center comes out clean.
Remove from oven and cool in the pan for 10 minutes. Transfer to a cooling rack to cool completely. Serve warm or at room temperature.