Mix the graham cracker crumbs, 1/2 cup of the white sugar, and the melted butter together. Press mixture into the bottom of one 9 or 10 inch springform pan.
In a large bowl, combine cream cheese, eggs and egg yolks; mix until smooth. Add the remaining 1 3/4 cups white sugar, the flour and the heavy cream. Blend until smooth. Pour batter into prepared pan.
Bake at 400 degrees F (200 degrees C) for 10 minutes, then turn oven temperature down to 200 degrees F (100 degrees C) and continue baking for 1 hour, or until filling is set. Let cheesecake cool, then refrigerate.