1Preheat oven to 350 degrees F (175 degrees C). Line 12 muffin cups with paper liners.
2Sift flour, baking powder, baking soda, and salt together in a bowl.
3Beat brown sugar, peanut butter, and 2 tablespoons butter together in a bowl using an electric mixer on medium speed until creamy, about 1 minute. Beat banana, eggs, and 1 1/2 teaspoons vanilla extract into creamed peanut butter mixture until incorporated, about 1 minute.
4Beat flour mixture, alternating with 1/2 cup milk, into creamed peanut butter mixture until batter is well combined; pour into muffin cups.
5Bake in the preheated oven until a toothpick inserted in the center of a cake comes out with moist crumbs, 20 to 23 minutes. Cool cupcakes in the tin for 15 minutes before transferring to a wire rack to cool completely.
6Beat marshmallow fluff, 2 tablespoons butter, shortening, and 1 teaspoon vanilla extract together in a bowl using an electric mixer until smooth. Gradually beat confectioners' sugar, alternating with 2 tablespoons milk, into marshmallow mixture until desired thickness is reached; chill in refrigerator until thickened, about 15 minutes.
7Spread frosting over cupcakes or pipe through a pastry bag.