Cream together 1/2 c. butter, sugar, and brown sugar in a stand mixer until smooth. Add egg and vanilla.
In a separate bowl, whisk together graham cracker crumbs, flour, salt, and baking powder.
Slowly add the dry mixture to the wet mixture on low speed until combined.
Spread dough into a greased 9x9 glass baking dish. Bake 20 minutes at 350°, or until lightly golden on top. Allow to cool.
Using an electric hand mixer, mix peanut butter, powdered sugar, and 4 Tbsp butter together. Press evenly onto cookie layer.
Place chocolate chips and 4 Tbsp butter in a microwave safe bowl. Heat for 30 seconds, stir, heat for 30 more seconds, and stir again till smooth and melted. Pour over peanut butter layer.
Allow to cool completely. Cut into bars to serve.