Preheat the oven to 325 F ( 160 C) and prepare a 9x3 inch spring form pan with a light coating of baking spray and line the bottom with parchment paper.
First, make the browned butter. Slice butter into chunks and place them into a medium skillet on medium heat. Allow butter to melt and cook through a foamy stage until fragrant. The butter will be an amber brown with dark brown speckles. Instantly remove from the heat and pour bitter into a heat proof bowl. Allow it to cool to room temperature.
In a medium bowl hand whisk together flour, baking powder, baking soda, salt and banana pudding powder. Set aside.
Using a separate large bowl, stir together dark brown sugar, sugar, brown butter, eggs, and vanilla. Add the mashed bananas and stir until evenly distributed.
Spoon in half of ⅓ of the flour mixture and pour in ½ cup of the milk. Using a hand held mixer on medium low speed, mix until incorporated. Repeat with remaining flour mixture and milk. Scrape bottom and sides of bowl as needed to grab any ingredients stuck to bowl.
Spoon batter into the prepared baking pan and center on the middle rack of the oven.
Bake cake for 60 minutes to 1 hr and 10 minutes until a toothpick inserted into the center comes out clean with just a few crumbs.
Place pan on a wire rack to completely cool before removing.
Transfer cake to serving dish and make the frosting.
Using a medium bowl stir together peanut butter and honey until smooth. Sift cocoa powder over top and add the heavy cream. Using a hand mixer on medium low speed, blend until smooth. Add a tablespoon of heavy cream if needed for a thinner frosting.
Spread frosting across banana cake, slice and serve.