1. To make the carrot cake batter, peel the carrots, then grate them just until you have 2 1/2 cups (250g) of grated carrots. Cover the grated carrot and set in the fridge.
2. Chop the remaining raw carrots (about 375g) into pieces small enough to go into a food processor or blender. Put chopped carrots in a steamer basket (or a colander, if you don’t have a steamer basket) set over a pot of boiling water. Cover and steam the carrots until very tender, about 10-15 minutes.
3. Put the warm carrots into a food processor or blender and puree (do not add the water used to steam the carrots, JUST the carrots). The puree will be thick. You should end up with about 1 1/4 cups (312g) of carrot puree. Set aside to cool while you make the cake batter.
4. Prepare a 9 inch springform pan with parchment paper circle in the bottom and grease the sides. Preheat oven to 350°F (176°C).
5. Combine the flour, baking powder, baking soda, salt and spices in a medium sized bowl and set aside.
6. Add the butter, oil, sugars and vanilla extract to and large mixer bowl and beat together until light in color and fluffy, about 1 1/2 to 2 minutes. Do not skimp on the creaming time, but do not over mix either.
7. Add the eggs one at a time, mixing until mostly combined after each. Scrape down the sides of the bowl as needed to be sure all ingredients are well incorporated.
8. Add half of the dry ingredients to the batter and mix until mostly combined.
9. Add the carrot puree (it can be room temperature or cold) and mix until well combined.
10. Add the remaining dry ingredients and mix until combined. Do not over mix the batter.
11. Stir in the grated carrots, pineapple, coconut, pecans and raisins (if using them all). Do not over mix. Set aside.
12. To make the cheesecake filling, mix the cream cheese, sugar, and flour in a large mixer bowl until smooth and combined (Use low speed to keep less air from getting into the batter, which can cause cracks). Scrape down the sides of the bowl.
13. Add the sour cream and vanilla extract. Beat on low speed until well combined.
14. Add the egg and beat on low speed to combine.
15. Preheat oven to 350°F (176°C). Line a 9-inch (23cm) springform pan with parchment paper in the bottom and grease the sides.
16. Add about 1/3 of the carrot cake batter and spread evenly, then add about half of the cheesecake filling.
17. Drop spoonfuls of another 1/3 of the carrot cake batter over the cheesecake filling and gently spread into an even layer.
18. Add the remaining cheesecake filling and spread into an even layer.
19. Drop spoonfuls of the remaining 1/3 of the carrot cake batter over the cheesecake filling and gently spread into an even layer.
20. Bake for 60 minutes or until the center of the cake is pretty well set, but still a touch jiggly.
21. Turn off the oven, but leave the oven door closed for 30 minutes.
22. Allow to cool on the counter for about 1 hour, then refrigerate until cold and firm. The top may crack a little bit, but that’s ok.
23. To make the frosting, add the cream cheese and butter to a large mixer bowl and beat until well combined. Set aside.
24. Add the heavy whipping cream, powdered sugar, vanilla extract and a pinch of salt to a large mixer bowl and whip until stiff peaks form.
25. Gently fold about half of the whipped cream into the cream cheese and butter mixture. Once mostly combined, add the remaining whipped cream and gently fold together until well combined.
26. Remove the cold and firm cake from the springform pan and place on a platter. Frost the cake with the frosting, then press chopped pecans into the sides and top the rim with some grated carrots, if desired.
27. Refrigerate the cake until ready to serve. Serve cold. Cakes is best when stored well covered for 3-4 days.