Preheat the oven to 325 degrees F (165 degrees C). Spray the bottom of an 8×8-inch metal baking pan with cooking spray.
Mix flour, cocoa, and 1/4 teaspoon plus a pinch of salt together in a bowl and set aside.
Melt butter in a medium saucepan over low heat. Add semisweet and bittersweet chocolate to melted butter and stir until smooth. Remove from heat; set aside for 2 to 3 minutes.
Meanwhile, mix brown sugar, eggs, and banana by hand until combined, about 1 minute. Add melted chocolate mixture to banana mixture and stir well, about 1 minute more. Mix flour mixture slowly into chocolate, stirring just enough to combine. Fold in walnuts and chocolate chips. Spread batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out with moist crumbs, 35 to 40 minutes. Remove from the oven and let cool in the pan on a wire rack for at least 2 hours before cutting.