Line a 9x9 baking dish with parchment paper, set aside.
Using either a stand mixer or a hand held mixer, combine the melted butter, powdered sugar and graham crackers.
Mix in the 1 1/4 cup of creamy peanut butter, just until well incorporated.
Evenly spread the peanut butter mixture into the bottom of the baking dish.
In a heat safe bowl, add the semi-sweet chocolate chips and the remaining 3 tablespoons creamy peanut butter. Heat for 30 second intervals, stirring well after each interval until the peanut butter and chocolate are smooth.
Spread the chocolate mixture over the peanut butter base.
Cut servings before you put the bars into the refrigerator. (The bars cut much easier this way).
Chill the bars for 1 hour.
Let the bars sit 10 to 15 minutes, at room temperature, before serving.