Mix the chocolate cookie crumbs with melted butter until evenly combined.
Press the mixture firmly into the bottom of an 8x8-inch baking dish.
Refrigerate the crust for 15 minutes.
Beat the cream cheese until smooth.
Mix in the powdered sugar and vanilla extract.
Fold in 1½ cups whipped topping until fluffy.
Spread the cream cheese mixture evenly over the chilled crust.
Whisk together the chocolate pudding mix and cold milk until thickened.
Spread the pudding evenly over the cream cheese layer.
Top with the remaining whipped topping.
Sprinkle with chocolate shavings and mini chocolate chips.
Refrigerate for at least 4 hours before slicing and serving.