Preheat the oven to 350 degrees and set a rack in the middle level. For the dough, in a bowl, cream together the butter and sugar until light and fluffy. Beat in the yolk until smooth.
In a separate bowl, combine the dry ingredients and gently fold them into the butter mixture with a rubber spatula. The mixture will be crumbly. Press the dough into the bottom of the prepared pan. Bake for about 20 minutes, until dry and golden. Cool the pastry layer. Lower oven temperature to 325 degrees.
For batter, beat cream cheese by machine on medium speed, until light. Beat in sugar, spices and puree, scraping bowl and beater(s) often. Beat in eggs and yolks, scraping often again. Scrape batter into prepared pan. Place pan on double square of foil and fold foil around pan bottom. Place springform in a small roasting pan and add an inch of warm water to roasting pan. Bake cheesecake about 50 to 60 minutes, or until slightly firm in center. Cool on a rack; wrap and refrigerate when cold.
To serve, remove springform side and slide cake to a platter.