Add sugar and cornstarch to a saucepan. Whisk together eggs and milk and add to saucepan. Heat over medium high, stirring constantly, until thickened. Remove from heat. Add vanilla extract. Let cool.

In a large bowl, stir together powdered sugar and peanut butter until crumbly.

Place half of the crumbs into the baked pie shell. Pour vanilla pudding over top. Cover with Cool Whip. Sprinkle remaining crumbs on top.

Place in the fridge to cool until set, about 3 hours.