1. To steam the carrots, bring about an inch of water to a boil in the bottom of a pot. Put peeled carrots in a steamer basket (or a colander, if you don’t have a steamer basket) set over the boiling water. Cover and steam the carrots until very tender, about 10-15 minutes.
2. Put the warm carrots into a food processor and puree. You should end up with a little less than a cup of carrot puree. Set aside to cool.
3. Preheat the oven to 350°F (176°C) and line a cupcake pan with cupcake liners.
4. To make the cheesecake batter, add the cream cheese and sugar to a large mixer bowl and mix on medium-low speed until smooth.
5. Add the sour cream, vanilla extract and cinnamon and mix until well combined.
6. Add the egg white and mix until well combined. Set aside.
7. To make the cake batter, cream the butter and sugar on medium speed in a large mixer bowl until light in color and fluffy, 3-4 minutes. Don’t skimp on the creaming time.
8. Add the vanilla extract and vegetable oil and mix until combined.
9. Add the eggs one at a time, mixing until incorporated after each addition.
10. Combine the dry ingredients in a medium sized bowl and add half of the dry mixture to the batter and mix until combined.
11. Add the carrot puree to the batter and mix until well combined.
12. Add the remaining flour mixture and mix until well combined and smooth.
13. Stir in the crushed pineapple and coconut flakes. Scrape down the sides of the bowl as needed to ensure everything is well combined.
14. To layer the cupcakes, add 1 tablespoon of cupcake batter to the bottom of each cupcake liner, spreading it so that it covers the bottom.
15. Add 1/2 a tablespoon of the cheesecake filling to the center of the batter.
16. Add another tablespoon of cupcake batter and another half tablespoon of cheesecake batter.
17. Top the cupcakes with another tablespoon of cupcake batter, then swirl everything around with a toothpick.
18. Bake the cupcakes for 16-18 minutes, or until a toothpick inserted in the middle comes out with a few crumbs.
19. Remove cupcakes from the oven and allow to cool for 2-3 minutes, then remove to a cooling rack to finish cooling. The centers may fall a bit as they cool, which is ok. It’s from the cooling of the cheesecake layers.
20. To make the frosting, beat the cream cheese and butter together in a large mixer bowl until well combined and smooth.
21. Slowly add the powdered sugar and mix until well combined and smooth.
22. Add the cinnamon and vanilla extract and mix until well combined.
23. Pipe the frosting onto the cooled cupcakes and garnish with a sliver of carrot. I used a vegetable peeler to create mine.
24. Refrigerate the cupcakes until ready to serve. Cupcakes are best when stored well covered in the fridge for 3-4 days.