In a medium bowl, whisk the sugars and salt together.
Melt the butter in a small bowl in the microwave. Stir the peanut butter into the melted butter until the peanut butter melts into the butter.
Stir the peanut butter mixture into the sugar mixture. Add the flour and stir until a crumbly dough forms. Set aside.
Make the banana bread cake.
Preheat the oven to 325°F. Place the butter in an 8 inch x 8 inch baking pan and set it in the oven to melt.
In a large bowl, mash bananas using a potato masher or the backside of two forks. Add sugar and stir to combine. Add flour, baking powder, and baking soda and stir to combine. Add egg and stir to combine.
Remove the pan with the butter from the oven. Carefully tilt the pan to coat the sides with the melted butter, then pour the melted butter into the bowl with the banana mixture and stir to combine.
Pour the banana mixture into the pan and top with the crumb mixture. Gently press the crumbs down into the dough.
Bake the cake.
Bake the cake for one hour, until a stick inserted into the center of the cake comes out clean. Let the cake cool in the pan.
Once it's cool (or nearly cool), dust the cake with powdered sugar and slice into 9 squares to serve.
Notes
Storage: Store in an airtight container at room temperature for up to 4 days.