For the crust, mix together the graham crackers with the sugar, cinnamon, nutmeg, and cloves. Stir in the butter and mix well. Into a 9" springform pan, press in the crumbs and work up the sides for about 1 3/4". Freeze crust for 10 min.
Preheat oven to 375F having a rack positioned in the middle. Bake crust for 8 min. Remove the crust from the oven and let cool while you make the filling.
For the filling, in a large bowl of a standup mixer beat the cream cheese with the sugar. Add in the rum, brandy, vanilla, cinnamon, and nutmeg. Beat well to combine. Add in the eggs, one at a time, beating well after each addition.
Spoon filling into crust and bake for 45 min. or until softly set in the center. If the top begins to brown too much cover it with foil. Take the cheesecake out and allow to cool for 30 min.
Increase oven temperature to 400F.
For the topping, whisk the sour cream, sugar, and vanilla in a medium bowl. Pour mixture carefully over cheesecake. Bake until set for 8 min. Let cheesecake cool completely then cover and refrigerate overnight.
To serve, cut around the edge of the cheesecake to loosen and then release. Slide cheesecake carefully onto a serving dish, removing the bottom pan. Sift the cinnamon and nutmeg on top and decorate with the cinnamon sticks.