In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and peanut butter until combined, scraping down the sides of the bowl as needed. Add the powdered sugar and graham cracker crumbs, mixing until smooth.
Line a quarter baking sheet (or 13x9-inch baking pan) with wax paper so that it hangs over on two sides. Transfer the peanut butter mixture into the pan. Using an offset spatula, spread the mixture into an even layer. (The easiest way to do this is to coat the spatula with cooking spray then spread the mixture.)
Melt the chocolate chips in a double-boiler or a microwave, stirring until smooth.
Pour the melted chocolate over the peanut butter mixture then spread it into an even layer.
Refrigerate the bars until the chocolate hardens slightly about 10 minutes. Before the chocolate has fully hardened, remove the bars from the fridge and cut them into 1-inch squares. Return the bars to the fridge and continue chilling until the peanut butter mixture has firmed up, a minimum of 2 hours and up to overnight.