Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, sift together the all-purpose flour, unsweetened cocoa powder, baking soda, baking powder, and salt. Set aside.
In a large bowl, cream the softened unsalted butter and granulated sugar together until light and fluffy using an electric mixer.
Add the eggs one at a time to the butter and sugar mixture, beating well after each addition.
Mix in the vanilla extract.
Add the mashed ripe bananas and sour cream to the wet mixture, stirring until combined.
Gradually add the dry ingredients to the wet ingredients, mixing gently until just combined. Do not overmix.
Fold in the semi-sweet chocolate chips evenly into the batter.
Pour the batter into the prepared cake pan and spread it evenly.
Bake in the preheated oven for 40 to 45 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.