In a mixing bowl, combine the shortbread cookie crumbs with melted butter. Mix with a fork until evenly coated. Press the mixture firmly into the bottom and sides of a 9-inch pie plate. Chill while preparing the filling.
Beat the cream cheese in a bowl until smooth. Add peanut butter, sugar, and vanilla extract, mixing until fully combined.
Fold in 8 ounces of Cool Whip gently with a spatula. Spread the filling evenly into the chilled crust.
Melt the semi-sweet chocolate in a microwave in 30-second intervals, stirring each time. Fold in 1 cup of the remaining Cool Whip.
Spread the chocolate mixture evenly over the peanut butter filling.
Refrigerate the pie for at least 4 hours or preferably overnight to set fully.