Preheat the oven to 350°F / 175°C. Butter and line an 8" square pan* with parchment paper.
In a small microwave safe bowl, melt the butter in 20 second intervals, stirring after each interval until it's just completely melted.
In a medium sized mixing bowl, mash the banana. Add in the melted butter, sugar, eggs, vanilla, and sour cream. Whisk vigorously until the mixture is well combined.
Add in the flour, espresso powder, baking powder, and salt. Whisk together until only a few flour streaks remain. Add in the chocolate chips, then mix just until no flour streaks remain.
Pour the cake batter into the prepared cake pan. Bake for 25-30 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Mocha Cream Cheese Frosting
In a large mixing bowl, with a hand or stand mixer, beat together the cream cheese, butter, and salt until the mixture is light and fluffy.
Add in half of the powdered sugar and beat until combined. Then, beat in the rest of the powdered sugar along with the cocoa powder and espresso powder.
Beat on low speed for 2 minutes, or until the mixture is well combined.
Once the cake has fully cooled to room temperature, top it with the frosting. Slice, serve, and enjoy!
Notes
*You can also use an 8" circle pan, or a 9" circle pan. Note that it may take a little less time to bake in a larger pan, and it will be thinner.