Prepare the Oven and Pan
Preheat your oven to 350°F (175°C).
Grease a 9×13-inch cake pan with butter, ensuring all sides are well-coated.
Mix the Dry Ingredients
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a small separate bowl, combine the brown sugar and cinnamon for the filling and topping.
Start the Batter
In a stand mixer or a large bowl with a hand mixer, cream the butter and sugar on medium-high speed until light and fluffy, about 2 minutes.
Add the eggs one at a time, mixing well after each addition.
Mash the bananas and add them to the batter along with the vanilla extract. Mix until smooth but slightly chunky.
Combine the Wet and Dry Ingredients
Reduce the mixer speed to low and add one-third of the flour mixture, mixing until just combined.
Add half of the sour cream and mix until incorporated.
Repeat the process with the remaining flour and sour cream, ending with the last portion of dry ingredients. Avoid overmixing.
Layer the Cake Batter
Pour half of the batter into the prepared pan and spread it evenly using an offset spatula or spoon.
Sprinkle half of the brown sugar-cinnamon mixture over the batter, followed by half of the chocolate chips.
Dollop the remaining batter over the filling and spread it evenly.
Top with the rest of the brown sugar mixture and chocolate chips.
Bake the Cake
Place the pan in the preheated oven and bake for 40 minutes, rotating halfway through.
The cake is done when the top is golden brown and a toothpick inserted in the center comes out with a few moist crumbs but no wet batter.
Cool and Serve
Let the cake cool completely in the pan on a wire rack before slicing.
Serve as is or with a scoop of vanilla ice cream for an extra treat.