Place a fine mesh sieve over a bowl then set aside. Add sugar, cornstarch, and salt to a saucepan then whisk to combine. Add 1/4 cup milk then whisk until smooth. Add egg yolks then whisk until smooth. Add remaining 1 cup milk then whisk to combine. Turn heat to medium then cook while slowly whisking until pudding thickens and starts to barely bubble, 6 minutes - this will happen all of the sudden. Turn heat down to low then switch to a spatula and continue to cook while stirring until pudding is very thick, 2 minutes. Take pan off heat then stir in butter and vanilla until melted.

Pour pudding through the fine mesh sieve to catch any bits of cooked egg. Cover the top of the pudding with plastic wrap to prevent a skin from forming on top then refrigerate until completely chilled. Can be made several days ahead of time.

Add whipped topping to the chilled pudding then fold to combine. Add crushed Oreos then fold to combine. Refrigerate for at least 4 hours before serving.