Pre-heat oven to 180°C (350°F). Line the inside of a 6-inch cake pan with parchment paper and set aside.
Make the frosting by mixing together the cream cheese, 0 calorie icing sugar and vanilla extract until smooth. Set aside in the fridge whilst making the cake.
To make the cake, whisk together the egg and 0 calorie brown sugar until light and fluffy. Add the yogurt, applesauce and vanilla extract and whisk until smooth.
Add the flour, spices, baking powder and shredded carrot and whisk to combine.Transfer the batter to the lined cake pan and bake for 20 minutes or until a toothpick inserted into the centre comes out with a few crumbs.
Allow the cake to cool completely.Frost the cooled cake, cut into 4 slices and enjoy!
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Notes
*0 calorie brown sugar - can be subbed for any granulated 0 calorie sweetener (1:1 ratio with sugar)*0% fat greek yogurt - can be subbed for any fat-free yogurt including dairy-free*Unsweetened applesauce - can be subbed for an equal amount of yogurt*Philadelphia lightest - can be subbed for low fat cream cheese *0 calorie icing sugar - can be subbed for regular icing sugar