Heat oven to 350 degrees. Combine graham crackers, butter and 2 tbsp of the sugar. Press into bottom and 1 inch up side of a 9-inch springform pan or a Push Pan. Bake at 35 degrees for 10 minutes. Cool slightly.
In a bowl, beat cream cheese until smooth. In a small bowl, blend remaining 2/3 cup sugar, the cornstarch, cinnamon and nutmeg. On low speed, beat into cream cheese. Increase speed to medium; beat in egg, then yolks. Beat in milk and rum flavoring.
Pour filling into crust, spreading level. Bake at 350 degrees for 45 minutes, or until just set in center. While warm, run a thin spatula between pan and crust. Cool to room temp and refrigerate until serving.