In the bowl of an electric mixer fitted with the paddle attachment, combine the confectioners' sugar, butter, vanilla, and milk, and beat until light and fluffy, about 3 minutes, scraping down the bowl with a rubber spatula as necessary. Add the peanut butter and mix until combined.

Use the frosting immediately, if possible. It may be stored in an airtight container at room temperature overnight, or in the refrigerator for up to 4 days. Let he frosting come to room temperature and briefly rebeat it in the mixer before using.

Recipe makes enough to generously frost a 9-inch (2 layer) cake, a 9- by 13-inch cake, or 2 dozen cupcakes.