Line a 9x13 pan with foil and set aside.
In a food processor, pulse graham crackers to a fine crumb. Add melted butter, powdered sugar, brown sugar and peanut butter very well and pulse until thoroughly combined. Press mixture evenly into the bottom of prepared baking pan.
In the microwave or on the stove top, melt chocolate chips with peanut butter until completely smooth. If using the microwave, use 30 second increments to ensure the chocolate doesn't scorch. Spread chocolate mixture on top of the peanut butter layer until completely smooth. Allow bars to set in the refrigerator for 3 hours.
These peanut butter cup bars will keep for up to 5 days stored in an airtight container in the refrigerator.