Preheat oven to 350°. Line your muffin cups with paper liners.
Whisk together flour, baking powder, baking soda, and salt in a medium bowl and set aside.
In the bowl of an electric mixer fitted with a paddle attachment, beat the peanut butter, butter, and brown sugar until creamy. Add vanilla, eggs, and banana and beat until well combined. Gradually mix in flour mixture, alternating with milk, making sure to scrape the sides of the bowl, until the batter comes together.
Divide batter evenly among 12 muffin cups. Bake for about 20 minutes, until a toothpick inserted in the center comes out clean. Let sit in pan about 10 minutes, then transfer to a cooling rack to cool completely before frosting.