Heat the oven to 320°F (160°C), using static mode (no fan). Line a 9x13-inch baking dish with parchment paper.

In a food processor, pulse the cookies until finely ground. Stir in the melted butter until evenly combined and the mixture resembles wet sand. Press into the prepared baking dish, smoothing into an even layer. Chill while preparing the filling.

In a large bowl, combine the white cheese, sour cream, sugar, eggs, heavy cream, vanilla pudding mix, cornstarch, and vanilla extract. Whisk until smooth, or use a stand mixer fitted with the whisk attachment. Pour over the chilled crust and smooth the top. Bake for about 1 hour, or until the edges are set and the center still has a slight wobble. Turn off the oven and let the cheesecake cool inside with the door slightly ajar for 15 minutes, then transfer to a wire rack. Once fully cooled, refrigerate for at least 2 hours.

In a stand mixer fitted with the whisk attachment, beat the heavy cream and vanilla pudding mix until stiff peaks form. Spread the whipped topping evenly over the cheesecake.

Sprinkle generously with grated white chocolate and refrigerate for at least 2 to 4 more hours before serving.