Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch springform pan.
In a medium bowl, mix graham cracker crumbs, 3 tablespoons sugar and melted butter. Press into the bottom of the greased springform pan.
In a large bowl, beat cream cheese until smooth. Gradually beat in 1 cup of sugar and the flour. Beat in vanilla and cream until blended. Add eggs one at a time, beating well after each addition.
Pour batter into prepared pan. Bake in preheated oven for 40 minutes. Turn oven off and let cake cool in oven with the door closed for 5 to 6 hours; this prevents cracking.