Preheat the oven to 350 degrees F. Line a 9X13-inch pan (I use a metal pan) with parchment paper with overhanging edges to make it easier to lift and cut the bars. Lightly grease the bottom and sides with cooking spray and set aside.
For the carrot cake batter, in a medium bowl, whisk together the flour, cinnamon, baking powder, baking soda, nutmeg and salt. Set aside.
In another medium bowl, whisk together the granulated sugar, brown sugar, eggs, oil and vanilla until very well-combined and lighter in color, 1-2 minutes.
Add the dry ingredients and then the carrots and mix until no dry streaks remain (don't over mix).
For the cheesecake batter, whip the cream cheese and granulated sugar with an electric mixer (handheld or stand mixer) until smooth and well-combined, 1-2 minutes. Add the sour cream, eggs and vanilla and mix for another minute or so until evenly combined, scraping down the sides of the bowl as needed.
Spread half of the carrot cake batter in a thin layer on the bottom of the prepared pan. Spoon the cheesecake batter and remaining carrot cake batter over the top, alternating heaping dollops so there's an even amount of batter across the bars.
Use a knife to lightly swirl the batter together (see pictures in the post). Bake the bars for 35-40 minutes until the top springs back lightly to the touch. Let cool completely. Serve at room temperature or chilled (these bars can be made 1-2 days ahead of time; refrigerate until serving).
Substitutions: you can replace half of the oil with applesauce with good results. Full fat cream cheese works better than light cream cheese in this recipe (light cream cheese is runnier and doesn't produce as sturdy of a cream cheese swirl/layer).Tip: take care not to over mix either the carrot cake or cheesecake batter.Ratios: this recipe is prominent on the cheesecake so if you want more cake to cheesecake ratio - consider 1 1/2-ing the cake part.