Prepare the carrot cake batter by adding the flour, baking soda, baking powder, salt, cinnamon, and nutmeg into a medium bowl and whisk to combine. Set aside.
In the bowl of a stand mixer equipped with a whisk attachment, add the vegetable oil, applesauce, granulated sugar, brown sugar, egg, and vanilla. Whisk until combined and lighter in color.
Add the dry ingredients into the wet and mix until there are no dry spots remaining. Fold in the shredded carrots with a spatula until evenly distributed throughout the batter.
Pour about ⅓ of the cake batter into the bottom of the springform pan and smooth. Use a large spoon to dollop about ⅓ of the cream cheese mixture on top, do not swirl. Continue with two more layers ending with the cake batter.
Cover the springform completely in aluminum foil and make sure to seal around the top edges of the pan as best as you can to keep any extra moisture out.
Add about 1 cup of water and a trivet to the inner pot of your Instant Pot and place the cheesecake on the trivet. Seal the lid and set on high manual pressure for 60 minutes with a 10 minute natural release. Once you can open the Instant Pot, remove the cheesecake and remove the aluminum foil and allow the cheesecake to cool to room temperature. Once it has cooled, transfer to the refrigerator to set overnight, or at least 6 hours.