Preheat oven to 350°F. Spray 9x9 square cake pan with non-stick spray.
Mash your bananas and set aside.
Using either an electric hand mixer or stand mixer, mix together the melted butter and brown sugar.
Add in the vanilla, eggs and mashed banana.
Add the flour, baking soda and salt to the bowl. Slowly incorporate the dry ingredients until just combined. Do not over mix.
Pour into prepared cake pan. Bake at 350° F for 35-45 minutes. It should pass the toothpick test before taking out of the oven.
While the cake is baking, brown your butter for the frosting.
In a small sauce pan, heat your butter on low, stirring constantly until the color of the butter turns a golden brown and it gives off a nutty aroma.
Immediately transfer the brown butter to a cool bowl or container to stop the cooking so the butter doesn't burn.
Allow the butter to sit until close to room temperature and then place in the fridge for approx 30 minutes, or until the butter is almost back to it’s solid form.
Once the butter is back to being mostly solid, it is time to make the frosting. At this point, your cake should be out of the oven.
In the bowl of a stand mixer, cream together the brown butter and cream cheese until mixed thoroughly.
Scrape the sides of the bowl and then alternate adding the remaining ingredients, adding a portion of the powdered sugar and then some liquid, letting the mixer go on low until the powdered sugar is completely incorporated before adding more.
Repeat this process until all of the ingredients have been added. You can adjust the consistency of the frosting by adding more heavy cream to this the frosting or more powdered sugar to thicken the frosting.
Spread on top of your banana cake. Slice and serve.
Notes
You can double this recipe and bake in a 9x13 pan.