Finely crush the shortbread biscuits or graham crackers using a food processor or by placing them in a sealed bag and crushing them with a rolling pin.
Mix the biscuit crumbs with the melted butter until evenly combined.
Firmly press the mixture into the bottom of a 7-inch (18 cm) springform pan using the back of a spoon or the bottom of a glass.
Refrigerate the crust while preparing the filling.
In a large mixing bowl, combine the cold heavy cream, softened cream cheese, sifted powdered sugar, and vanilla extract.
Using an electric mixer, beat the mixture until thick, smooth, and fluffy. The consistency should resemble soft ice cream and hold its shape.
Spoon the cheesecake filling over the chilled crust.
Smooth the top using an offset spatula or the back of a spoon.
Cover the pan and refrigerate for at least 4 hours, although overnight chilling provides the best texture and flavor.
Carefully remove the cheesecake from the springform pan.
For clean slices, dip a sharp knife in hot water and wipe it dry between each cut.
Serve plain or garnish with fresh berries, whipped cream, fruit compote, caramel sauce, or chocolate shavings.