Preheat oven to 350 degrees. Grease a 9-inch pie pan. Place whole Oreos in a food processor and grind into fine crumbs. Transfer crumbs to a bowl and add sugar and melted butter. Use a fork to mix together evenly. Dump into greased pie pan and press crumbs firmly into the pie pan and up the sides to form a packed crust.
Bake crust in preheated over for 9 minutes. Remove from oven and let cool completely before adding the filling.
Place cream cheese in the bowl of a stand mixer. Using a paddle attachment, beat until fluffy and all lumps are gone, about 2 minutes. Add Nutella and whip together with vanilla and salt until smooth, about 2 more minutes.
Using a spatula, fold in 3/4 of the whipped topping. Pour into cooled pie crust. Place in freezer to chill for 4 hours.
Before serving, top with the rest of the whipped topped. Add chocolate shavings for garnish. Slice and serve.