Crush the Oreo cookies into fine, even crumbs, then stir them with the melted unsalted butter until every crumb looks lightly moistened.

Divide a small portion of the cookie mixture among six parfait glasses and press it gently into the bottoms to form the first layer.

Whisk the instant chocolate pudding mix with the cold whole milk and Baileys Irish Cream for about 2 minutes, until thickened. Let the pudding stand for several minutes so it can fully set.

Beat the softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy, scraping the bowl as needed so no cream cheese lumps remain.

Fold approximately half of the thawed whipped topping into the cream cheese mixture using a gentle motion. Stop as soon as the filling is fluffy and evenly combined.

Spoon or pipe the cream cheese mixture over the cookie crumbs in each glass, dividing it as evenly as possible for consistent layers.

Add a layer of the Baileys chocolate pudding over the cream cheese filling. Follow with another small layer of cookie crumbs or whipped topping, depending on whether you prefer a more textured or cream-forward presentation.

Finish each parfait with the remaining whipped topping, then scatter chocolate shavings or mini chocolate chips over the top.

Cover the glasses and refrigerate for at least 1 hour before serving. For the best texture and flavor, chill them for 2 to 4 hours.