Start by lining your 9x13 inch baking pan with parchment paper, leaving a little overhang on the sides for easy removal later.
In a large mixing bowl, combine the creamy peanut butter, softened unsalted butter, salt, powdered sugar (start with 2 cups), and vanilla extract. Mix well until smooth and fully combined. Add more powdered sugar if you prefer a sweeter bar.
Crumble the graham cracker sheets into fine pieces by placing them in a zip-top bag and crushing with a rolling pin. Add the crumbled graham crackers to the peanut butter mixture and stir until well incorporated.
Transfer the peanut butter and graham cracker mixture into the prepared baking pan. Use a spatula to press it down evenly into the bottom, creating a solid base.
In a double boiler or microwave-safe bowl, combine the chocolate chips and shortening. Heat in 30-second intervals if microwaving, stirring in between, until the chocolate is completely melted and smooth.
Pour the melted chocolate over the pressed peanut butter mixture in the pan. Use a spatula to spread it evenly across the top.
Refrigerate the bars for at least 2 hours, or until the chocolate has set and the mixture feels firm to the touch.
Carefully lift the bars out of the pan using the parchment paper. Cut into squares or rectangles and serve.