Make the carrot cake: Shred carrots by hand or in a food processor, then set aside in a small bowl.
3. Step
In a large bowl, combine brown sugar, powdered sugar, and eggs and whisk until smooth.
4. Step
Add the oil and whisk to combine.
5. Step
Add the vanilla, flour, baking powder, cinnamon, nutmeg, and shredded carrots and stir with a spatula to combine.
6. Step
Make the cheesecake: In a separate large bowl, whisk together the cream cheese and powdered sugar until smooth.
7. Step
Whisk in the eggs, 1 at a time. Add the vanilla and sour cream and whisk until well blended.
8. Step
Pour ¾ of the carrot cake batter into a greased 8-inch springform pan and smooth the top. Add ½ of the cheesecake batter, then the rest of the carrot cake batter and cheesecake batter.
9. Step
Bake for 45 minutes, or until the cheesecake is set. Remove from the oven and let cool to room temperature, about 1 hour. Refrigerate for 4 hours, or overnight.
10. Step
Release from the springform, then slice and serve.
