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, beat the softened unsalted butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Mix in the mashed ripe bananas and sour cream until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Fold in the semi-sweet chocolate chips gently.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 40-45 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. Then transfer the cake to a wire rack to cool completely before serving.