In a large bowl, beat heavy cream, powdered sugar, and vanilla extract until stiff peaks form.
If using cream cheese, beat it into the whipped cream until smooth.
Spread a thin layer of whipped cream on the bottom of an 8x8-inch baking dish.
Arrange a layer of Oreo cookies over the cream. Break cookies as needed to fill gaps.
Spread one-third of the whipped cream mixture over the cookies.
Repeat the layers of Oreos and whipped cream until all ingredients are used, finishing with whipped cream on top.
Sprinkle crushed Oreos and chocolate shavings over the top.
Cover and refrigerate for at least 6 hours or overnight.
Slice and serve chilled.