Prepare the pan: Line an 8×8-inch baking pan with parchment paper, leaving some overhang for easy removal.
Make the peanut butter base: In a mixing bowl, combine melted butter, peanut butter, powdered sugar, vanilla extract, and graham cracker crumbs. Mix until smooth and well incorporated.
Press into the pan: Transfer the peanut butter mixture into the lined baking dish. Use a spatula to press it evenly and firmly into the pan.
Melt the chocolate: In a microwave-safe bowl, melt the chocolate chips in 20-second intervals, stirring in between until smooth. Alternatively, melt on the stovetop using a double boiler.
Spread the chocolate: Pour the melted chocolate over the peanut butter base. Smooth it out with a spatula.
Chill: Refrigerate the bars for at least 2 hours, or until fully set.
Slice and enjoy: Once chilled, lift the bars out of the pan using the parchment paper. Cut into squares and serve!