Heat 4½ cups of the milk in a large saucepan over medium heat until the milk is scalded (180°F).
Whisk in the flour, sugar, salt, vanilla, egg yolks, and the remaining 1½ cups cold milk.
Heat the milk mixture until thick, stirring continuously. Remove from the heat and allow to cool. Fold in the whipped topping.
Spread some peanut butter between two chocolate chip cookies to form a cookie sandwich.
Repeat until all four dozen cookies have been used. Cut or crumble the cookie sandwiches into the pudding mixture, and stir until well combined.
