Preheat oven to 350°F. Grease or lightly spray a 9 x 13 inch cake pan with nonstick spray.
Whisk together flour, sugar, baking powder, baking soda, and salt in a large bowl.
Add mashed bananas, buttermilk, shortening, eggs, and vanilla to the bowl. With an electric mixer, beat on low-speed until ingredients are combined, scraping sides of bowl as needed, about 1 minute.
Increase to medium speed and beat for 3 minutes. Fold in chocolate chips.
Spread cake batter into prepared pan and bake for 30 to 35 minutes or until a toothpick inserted into center of cake comes out clean or with crumbs.
Cool completely before frosting.
Frosting:
In large bowl, using an electric mixer, beat together cream cheese, butter, vanilla, and milk until smooth.
Add cocoa powder and powdered sugar (one cup at a time) and continue to beat on low speed until frosting is smooth and is desired consistency. Spread on cooled cake.
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Notes
Buttermilk substitute: Add 1 tablespoon white vinegar to ½ cup of milk, stir and let set for 2 minutes.
Frosting note: This makes a pretty big batch of frosting. It's actually enough to frost a layer cake. If you prefer less frosting, make a half batch by cutting the frosting ingredients in half.
Cake with cream cheese frosting should be stored in the refrigerator.