Preheat oven to 350F and line mini cupcake cups with mini cupcake liners. Set aside.
In medium-sized bowl, whisk together flour, baking powder and salt and set aside.
In KitchenAid or with electric hand mixer, cream together butter, sugars and peanut butter.
Beat in eggs, one at a time and scrape down the sides of the bowl to ensure ingredients are all incorporated.
Stir in vanilla extract.
Add flour mixture and milk, alternating (add approximately ¼ of the flour mixture then approximately ¼ of the buttermilk, stirring until just combined after each addition. Once the last of the flour/buttermilk has been added, scrape down the sides and the bottom of the bowl with a spatula and stir again until ingredients are completely combined.
Divide batter into prepared mini-cupcake tin, filling each liner ¾ full (I use a 1 ½½" cookie dough scoop for this, it makes the process very clean and easy).
Bake on 350F for 14 minutes (a toothpick inserted in center of cupcake should come out mostly clean or with dry crumbs).
Allow cupcakes to cool completely before frosting.
Frosting
In a microwave-safe bowl, microwave chocolate chips at 15 second intervals, stirring between intervals, until chips are completely melted. Set aside and allow to cool slightly.
In KitchenAid (or with electric hand mixer) cream butter.
Add sugar gradually until well-combined (scrape down bottom and sides of bowl as needed).
Stir the milk chocolate (it should be melted but should not be too hot) and add it to your butter/sugar mixture.
Beat on medium-speed until well-combined.
Stir in vanilla extract.
Add heavy cream, increase speed to medium-high and beat until well combined (about one minute).
Pipe or spread on to completely cooled cupcakes.
Notes
*A good substitute for buttermilk (one that I use often) would be ½ cup regular full-fat milk with ½ Tbsp (1½ tsp) vinegar or lemon juice stirred in and allowed to sit for 5 minutes before using