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Preheat oven to 350 F. Line a 9x13 baking pan with parchment, overhanging edges to make it easier to lift and cut bars. Lightly grease the bottom and sides with cooking spray and set aside.
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For the carrot cake batter, in a medium bowl, whisk together the flour, cinnamon, baking powder, baking soda, nutmeg and salt. Set aside.
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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.
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Add the dry ingredients and then the carrots and mix until no dry steaks remain but don’t over mix!
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For the cheesecake batter, whip the cream cheese and granulated sugar with an electric mixer until smooth and well-combined, 1-2 minutes. Add the sour cream, eggs, and vanilla and mix for another minute until evenly combined, scraping down the sides of the bowl as needed.
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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.
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Use a knife to lightly swirl the batter together. 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. If making ahead of time, refrigerate until serving.