Preheat the oven to 350F.
Butter a 9″ springform pan and set aside.
In a medium bowl, whisk together the sugar and 1 1/2 tsp flour.
Add the cream cheese and mix with an electric mixer until well combined, about 1 minute on low speed.
Add in eggs one at a time.
Add in the vanilla.
Add in the sour cream.
In a medium mixing bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon and nutmeg.
In a second medium mixing bowl, cream together the canola oil, applesauce, sugar, brown sugar, eggs, and vanilla.
Slowly combine the dry ingredients into the wet, just until combined.
Stir in the grated carrots.
Pour 1 1/2 cups of the carrot cake mixture into the buttered springform pan and spread evenly.
Dollop about 1/3 of the cream cheese mixture by spoonfuls over the carrot cake (don’t spread or swirl, just dollop it).
Spoon the remaining carrot cake mixture over the cream cheese layer,.
Drizzle the rest of the cheesecake mixture over the carrot cake mixture, working to cover all the carrot cake mixture.
Bake in a preheated oven for 60-65 minutes (you can tent with foil after 40 minutes if it looks like the top is getting too brown).
Remove from the oven and allow to cool on a wire rack for 1 hour.
Cover with foil and chill in the fridge overnight.
In a mixing bowl, whip together the cream cheese and butter until smooth.
Add the remaining ingredients and mix until pale and fluffy, about 4 minutes.
Spread evenly over the cheesecake.
Sprinkle the pecans around the edge.
Chill in the fridge at least an hour.
Slice and Enjoy!