Preheat oven to 325 degrees and grease a 9x13 pan.
In a medium bowl, whisk together all dry ingredients (flour through salt). In another bowl, use an electric mixer to cream together the sugar and butter until light and fluffy, about five minutes. Beat in the egg until thoroughly combined. In a small bowl or measuring cup, whisk together the buttermilk, oil and vanilla. Stream mixture into the butter mixture while beating on low. Increase speed to high and beat for 5-6 minutes until mixture is pale and homogenous. It may look a little grainy, but you want the mixture to be as smooth as possible.
Once the mixture is homogenous, add the banana and beat until bananas are broken up. Add the dry ingredients and mix on low until dry ingredients are just barely incorporated and you can still see streak of flour--do not overmix! Fold in the chocolate chips with a spatula and finish mixing the batter by hand until no floury streaks remain.
Pour batter into prepared pan and bake for 40-50 minutes (check at 40 minutes and continue baking for 5-7 minute increments until a tester inserted in the middle comes out clean. Cool completely before removing from pan.
Use a 6-inch cake ring or template to cut two 6-inch circles out of the cake. Line a six-inch cake pan with plastic wrap and press the remaining cake scraps firmly into the bottom to form your third cake layer. At this point, you can freeze tightly wrap each cake layer (leave the scrap layer in the cake pan) in plastic wrap for easier assembly later.