Preheat the oven to 350°F (175°C). Grease and flour an 8-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, 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 until fully incorporated.
Alternately add the dry ingredients and the buttermilk to the banana mixture, beginning and ending with the dry ingredients. Mix until just combined; do not overmix.
Fold in the semisweet chocolate chips gently.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake in the preheated oven for 35-40 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.
Turn the cake out onto a wire rack and let it cool completely before serving.