Combine graham cracker crumbs and melted butter in a medium bowl. Stir until the crumbs are evenly moistened.
Press the mixture firmly and evenly into the bottom of a 9-inch springform pan. Use the base of a glass or measuring cup to create a compact layer.
In a large bowl, beat softened cream cheese and sifted powdered sugar until smooth and creamy.
Add pure vanilla extract and mix to combine.
Whip cold heavy cream to stiff peaks and gently fold into the cream cheese mixture.
Stir in sour cream or Greek yogurt, if using, for extra tang (optional).
Transfer the mixture into the prepared springform pan and smooth the top with a spatula.
Cover and refrigerate for at least 4 hours or until fully firm.