Preheat oven to 400 degrees F (205 degrees C).
Mix graham cracker crumbs, melted butter, and 1/4 cup sugar together. Press mixture onto the bottom of one 9 or 10 inch springform pan. Place in freezer for 10 minutes.
Cream 3/4 cup of the sugar and cream cheese until smooth. Beat in eggs, vanilla, and cornstarch until just mixed. Stir in sour cream until blended. Pour into prepared crust.
Bake at 400 degrees for 10 minutes. Reduce temperature to 200 degrees and cook for 45 minutes. Turn oven off and leave cheesecake with door ajar for 3-4 hours.