Preheat the oven to 350°F and prepare two 8 inch round cake pans. Spray the inside with cooking spray, then cut round pieces of parchment paper so that they fit in the bottom of each pan (do not skip the parchment paper lining!).
Measure the butter, then place in a medium sized microwave-safe bowl and heat until melted. Whisk in both brown sugar and white sugar.
Add mashed banana, eggs, vanilla, and milk. Whisk until combined.
Mix in flour, salt, baking powder, and baking soda. Do not over-mix!
Divide the batter evenly between the two cake pans and bake on the middle rack of the oven for 25-35 minutes or until a toothpick inserted in the middle of the cakes comes out clean.
Let the cakes cool in the pans for 20 minutes, then run a butter knife around the outside of the cake to loosen it from the pan and flip upside down onto a cooling rack to cool completely.
Make the buttercream. In the bowl of a standing mixer or handheld mixer, beat butter and peanut butter together until combined. Slowly add in the salt and powdered sugar, mixing until combined.
Once the cake has completely cooled, assemble and enjoy.
