Beat the cold cream in a medium bowl until medium peaks form when the beaters are lifted. The tip will fall and the cream will have some consistency but not be firm. Don't overbeat it! You'll beat it longer when you incorporate it with the cream cheese mixture.
In a large bowl, beat the cream cheese with the granulated sugar until smooth. Add the powdered sugar and vanilla and beat again until smooth and well integrated.
Add half of the soft whipped cream and mix on low speed for 30 seconds.
Add the rest of the cream and mix on low speed until beginning to thicken. The peaks when you lift the beaters should be medium firm but with a slight drop.
Add the chopped Oreo cookies and fold them in with a spatula until integrated. Don’t overdo it; you want some chunks of cookies and speckled filling but not too much.
Pour the cheesecake filling into the prepared pan, smooth the top and refrigerate until firm, several hours.
When ready to serve, remove the pan from the fridge at the last minute so it's cold. To remove the cheesecake from the pan, place it on the serving plate and decorate with whipped cream rosettes or mounds around the edges (using a piping bag is better but not exclusive and store-bought cream can be used and is easier to use directly from the can) marking 8 servings. Top with halved regular Oreos or mini Oreos.