Combine Oreo cookie crumbs with melted butter until evenly mixed.
Press the crumb mixture firmly into the bottom and slightly up the sides of a 9-inch pie dish.
Refrigerate the crust for 15 to 20 minutes to set.
In a large bowl, beat cream cheese, powdered sugar, vanilla extract, and ¼ cup milk until smooth and creamy.
In a separate bowl, whisk instant chocolate pudding mix with 1½ cups cold milk until thickened, about 2 minutes.
Fold the prepared pudding into the cream cheese mixture gently until fully combined.
Fold in the thawed whipped topping until the filling is light and mousse-like.
Spread the chocolate mousse filling evenly over the chilled Oreo crust and smooth the top.
Refrigerate the pie for at least 3 to 4 hours to set completely.
Before serving, garnish with extra whipped topping and chocolate shavings or curls if desired.