Preheat the oven to 350°F. Line a 9x13 pan with parchment paper. Set aside.
Make the carrot cake batter: In a mixing bowl, whisk together the flour, baking soda, salt, cinnamon, nutmeg, and ginger.
In another bowl, whisk together the oil, white sugar, brown sugar, applesauce, vanilla and eggs.
Add the wet into dry, fold until almost all combined.
Stir in the carrots. Do not over mix. Set aside.
Make the cheesecake: beat the cream cheese and sour cream for 1-2 min, using a hand held mixer or stand mixer with the paddle attachment. Then add sugar and vanilla, mix again.
Then add eggs 1 at a time on medium low speed.
Pour half of the carrot cake batter into the prepared pan and spread evenly. It will seem like a thin layer, it's OK.
Dollop all of the cheesecake over the carrot cake.
Then spoon dollops of the remaining carrot cake batter over the cheesecake.
Swirl with a butter knife to get those big gorgeous swirls. Don't over do it though. Less is more!
Bake for 35-40 minutes.
*Note: when recipe testing, I noticed after baking and cooling, the top of the bars sunk and looked a little wonky because of the carrot cake swirl. Please be aware this might happen to yours too. Once cut into bars, it's not really noticeable and the swirls look so pretty, so I chose to keep the recipe like that. See recipe notes below if you want to layer the bars differently to get a more smooth top (but with no swirls on top).
Allow to cool completely at room temperature. Chill in the fridge for at least 3 hours or overnight.
Cut into squares, cleaning knife in between cuts (or you can run knife under warm water or even spray with non stick spray to get prettier slices) and enjoy!