Preheat oven to 375°F Line a baking sheet with parchment paper.
Whisk together flour, sugar, baking powder, and salt until thoroughly combined.
In a large bowl, beat together peanut butter, eggs, vanilla, and evaporated milk until evenly combined.
Add flour mixture and stir until just combined.
Stir in bananas.
Turn dough out onto a floured surface and knead it twice. Pat it into a 1-inch thick disk.
Use a 2 1/2 inch cutter to cut into rounds. Pat remaining scraps together, reroll, and cut out more. Transfer to a baking sheet and brush tops with evaporated milk.
Bake 20 minutes. Transfer to a cooling rack and allow to cool completely. Serve with strawberry jelly or marshmallow creme.