Line an 8×8-inch or 9×9-inch pan with parchment paper. Set aside.
In a large bowl, stir together the melted butter, peanut butter, and vanilla extract until smooth.
Add the confectioners’ sugar and stir until well combined. Stir in the graham cracker crumbs.
Press the mixture evenly into the prepared pan.
Place the chocolate chips and 3 tablespoons of peanut butter in a large microwave safe bowl. Microwave in 30 second burst, stirring each time, until just melted. Stir until mixture is smooth.
Pour evenly over the peanut butter base and smooth with a spatula. Sprinkle with flaky sea salt.
Place the pan in the refrigerator and chill until the bars are firm, about 2 hours.
Use a sharp knife to cut the bars into squares.