Line an 8 × 8-inch or 9 × 9-inch baking dish with parchment paper or aluminum foil, leaving enough material extending over the sides to assist with removing the finished bars.
Place the graham crackers in a resealable bag and crush them finely with a rolling pin. Alternatively, process them in a food processor until they form fine crumbs.
Add the melted and cooled unsalted butter and 1 cup of creamy peanut butter to a large mixing bowl. Stir thoroughly until the mixture is completely smooth.
Incorporate the confectioners’ sugar, mixing until no dry streaks remain. Gently fold in the finely crushed graham crackers until evenly distributed.
Transfer the peanut butter mixture to the prepared baking dish. Press and level the surface with a spatula to create a uniform base.
Combine the chocolate chips and the remaining ¼ cup of creamy peanut butter in a heatproof bowl.
Microwave the mixture in intervals of 20 to 30 seconds, stirring after each interval, until the chocolate and peanut butter have melted into a glossy, smooth topping.
Pour the chocolate-peanut butter mixture over the prepared base. Spread it evenly with a spatula, ensuring the entire surface is covered.
Refrigerate the assembled bars for at least 90 minutes, or until the chocolate layer has set completely.
Lift the chilled slab from the baking dish using the parchment paper or foil overhang. Place it on a cutting surface and divide it into squares or rectangular bars with a sharp knife.