Preheat the oven to 400 degrees F (205 degrees C).

Mix graham cracker crumbs, melted butter, and 1/4 cup sugar together in a medium bowl until well combined. Press mixture onto the bottom of a 9-or 10-inch springform pan. Place in the freezer for 10 minutes.

Beat cream cheese and remaining 3/4 cup sugar with an electric mixer in a large bowl until smooth. Beat in eggs, cornstarch, and vanilla until just combined. Stir in sour cream until blended. Pour into the prepared crust.

Bake in the preheated oven for 45 minutes. Turn the oven off and leave cheesecake in the oven with the door ajar for 3 hours. Place cheesecake in the refrigerator to cool completely, then remove it from the springform pan before slicing. Serve with your favorite topping.