Butter the bottom and sides of a 8×8-inch square pan. Put a long piece of parchment paper in the bottom of the pan, letting the parchment extend up two sides of the pan and overhang slightly on both ends. (This will make it easy to remove the bars from the pan after they have baked.) Butter the parchment.
Melt ½ cup of butter in a medium saucepan over low heat. Once melted, remove from heat and stir in the powdered sugar until smooth. Stir in the peanut butter and graham cracker crumbs until completely combined and smooth. Spread the peanut butter mixture into the prepared pan and smooth the top.
In the now-empty saucepan, melt the ¼ cup unsalted butter. Add the chocolate and stir until almost completely melted. Remove from heat and continue stirring until completely melted and smooth. Pour the melted chocolate over the peanut butter layer and smooth into an even layer.
Refrigerate for at least 30 minutes to set. Remove from the pan using the parchment overhangs and place on a cutting board. Use a pizza cutter to slice into 16 bars. Store in an airtight container in the refrigerator.