Preheat oven to 300 degree F. In a medium bowl stir together graham crackers, the 1/2 cup melted butter, and the cocoa powder. Press into the bottom of a 13x9x2-inch baking pan. Bake for 10 minutes. Cool completely.
In a medium saucepan cook and stir chocolate pieces and the 2/3 cup butter over low heat until melted. Carefully spread half of the chocolate mixture evenly over crust. Chill about 30 minutes or until chocolate is set. Cover remaining chocolate mixture; set aside at room temperature.
In a large bowl combine peanut butter, the 3/4 cup butter, and the vanilla. Beat with an electric mixer on medium speed until smooth.
Gradually beat in as much of the powdered sugar as you can with the mixer, beating on low speed. Stir in the remaining powdered sugar. Pat evenly onto chocolate layer in baking pan.
Spread remaining chocolate mixture evenly over peanut butter layer. Cover and chill for 2 hours. Cut into bars.