Line an 8x8-inch pan with parchment paper, leaving an overhang on the sides for easy removal.
In a large bowl, stir together the peanut butter, melted butter, graham cracker crumbs, powdered sugar, salt and vanilla until the mixture is thick and holds together like a thick dough.
Transfer the mixture to the prepared pan, pressing down firmly and evenly using a spatula or clean hands.
Chill the base for about 10 minutes while you prepare the chocolate topping.
In a microwave safe bowl, melt the chocolate chips and 2 tbsp peanut butter in 20-30 second increments, stirring well between each, until smooth and glossy.
Spread the melted chocolate evenly over the peanut butter base using a spoon or offset spatula. Refrigerate the bars for 2 hours or until the chocolate layer is firm and set.
Let the bars sit at room temperature for 10-15 minutes before cutting into bars. Store leftovers in a covered container in the fridge.