Preheat the oven to 350°. Line two muffin tins with 18 paper cupcake liners.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, and salt.
In a medium mixing bowl, whisk together the light brown sugar, sour cream, peanut butter, milk, oil, egg, and vanilla extract.
Create a well in the flour mixture and pour in the peanut butter mixture. Whisk until completely combined.
Divide the batter evenly between the paper liners (about ¼ cup per well).
Bake for 22 minutes or until a wooden toothpick inserted into the center comes out with a few moist crumbs. Let cool completely.
In a large mixing bowl or the bowl of a stand mixer fitted with the whisk attachment, combine the peanut butter and butter. Beat on medium-high speed until smooth and well combined, about 1 minute.
With the mixer on low speed, add the confectioners’ sugar, ½ cup at a time, until completely combined. Stop and scrape down the sides occasionally.
Add the cream and vanilla. Increase speed to medium-high and beat until light and fluffy.
Transfer the frosting to a piping bag and pipe onto the cooled cupcakes.
