Use shortening or butter to grease a 9-inch springform pan. Put to the side.
Crust: Add the Oreos to a food processor and run at high speed until the Oreos are fine crumbs.
Gradually pour the melted butter into the food processor while running it at low speed. Make sure the butter and Oreo crumbs are well-mixed. (You may need to stir with a spoon or spatula.)
Pour the crumbs into the springform pan and press them firmly into the base. Place in the freezer for about 20 minutes.
Oreo Cheesecake Filling: In a large bowl, add the cream cheese and powdered sugar, and use an electric hand mixer to mix until there are no lumps.
Add the heavy whipping cream and vanilla extract and continue mixing until smooth.
Fold in the whipped topping with a wooden spoon or spatula, then add the crushed Oreos. Mix until the Oreos are well distributed.
Pour the cheesecake filling into the springform pan, and smooth it out evenly with a spatula.
Place in the refrigerator for at least 4 hours.
Top with whipped cream and halved Oreos, if desired, and serve chilled.