Adjust the oven rack to the lower middle position, pre-heat the oven to 350ºF (180ºC) and line a 9-inch (23cm) square baking pan with parchment/baking paper.
In a large bowl, whisk together the light brown sugar, oil, eggs and vanilla until well combined and smooth.
In a separate bowl, whisk together the gluten free flour blend, baking powder, baking soda, xanthan gum, salt, cinnamon, ginger and nutmeg.
Add the dry ingredients to the wet and whisk everything together into a smooth batter with no flour clumps.
Add the coarsely grated carrots and fold them into the batter until they're evenly distributed throughout.
In a large bowl using a balloon whisk, mix the cream cheese and yoghurt together until smooth.
Mix together sugar and cornstarch, and add them to the cream cheese mixture. Mix well until combined.
Add the egg, egg yolk and vanilla, and mix well until smooth.
Pour about ⅓ of the carrot cake batter in the centre of the lined baking pan, then add about ⅓ of the cheesecake filling on top and spread it out slightly.
Continue alternating the cake batter and the cheesecake filling in ever decreasing amounts, until you’ve used them all up.
Use a skewer or the end of a knife to swirl the cake batter and cheesecake filling around.
Gently tap the baking pan a few times on the counter to level off the surface.
Bake the assembled cheesecake bars at 350ºF (180ºC) for about 40-45 minutes or until they’re only slightly wobbly in the centre.
Allow the cheesecake bars to cool completely to room temperature before slicing and serving.
