Place melted unsalted butter and one cup of peanut butter in a large bowl. Beat together using an electric hand mixer until well combined.
Add the powdered sugar and continue beating with the hand mixer until well combined.
Add the graham cracker crumbs, one cup at a time, and beat well after each addition.
Line a 9x13 inch baking pan with parchment paper, then secure the parchment to the pan with some clips. Transfer the mixture to the prepared pan using a large ice cream scoop. Put on vinyl gloves and press the peanut butter mixture into the pan.
Place the semi-sweet chocolate chips and ¼ cup peanut butter in a microwave-proof bowl. Microwave 30 seconds at a time, stirring well after each heating, for a total of 1 minute and 30 seconds, or until the chocolate is melted and smooth.
Pour the melted chocolate over the peanut mixture in the pan and spread into an even layer, completely covering the peanut butter mixture.
Remove the clips from the pan and cover it tightly with aluminum foil. Refrigerate the pan for at least two hours or until the bars are firm and the chocolate topping is set.
After the bars are set, remove them from the pan by lifting out the parchment. Carefully remove the parchment from the bars and place them on a large cutting board, then cut it into squares. Store in an airtight container in the refrigerator.
Yield 24 servings