Crush the Oreo cookies into fine crumbs using a food processor, or place them in a sealed food-safe bag and crush them with a rolling pin. Reserve a small amount of coarser crumbs if you want extra texture on top.

Beat the softened butter, softened cream cheese, powdered sugar, and vanilla extract until the mixture is smooth, creamy, and free of lumps. Scrape the sides of the bowl as needed for an even filling.

In a separate bowl, whisk the two pudding mixes with the cold milk for about 2 minutes, or until the mixture thickens. Allow the pudding to become fully thick before combining it with the cream cheese mixture.

Fold the thickened pudding into the cream cheese mixture until evenly blended. Gently fold in the thawed whipped topping so the filling stays light and fluffy.

Layer about one-third of the Oreo crumbs in a large trifle bowl, 9-by-13-inch dish, or individual serving cups. Add half of the pudding mixture, followed by another third of the crumbs, the remaining pudding mixture, and the remaining crumbs.

Cover the dessert and refrigerate it for at least 4 hours, although chilling overnight gives the best texture. Add gummy worms just before serving so they remain colorful and appealing.