1.  Preheat the oven to 180°C (160°C fan-forced). Line a 23 cm square cake tin with baking paper, leaving an overhang on two sides to make the cake easier to lift out.
2. In a large bowl, whisk together the vegetable oil, sugar and applesauce until well combined. Add the eggs, one at a time, whisking well after each addition.
3. In a separate bowl, whisk together the dry ingredients and gently fold together into wet ingredients until almost combined.
4. Fold through the grated carrot until evenly distributed through the batter.
5. Pour the batter into the prepared tin and smooth the top. Bake for 30-40 minutes, or until a skewer inserted into the centre comes out clean or with just a few moist crumbs attached.
6. Leave the cake to cool in the tin for 15 minutes, then lift it onto a wire rack using the baking paper and allow it to cool completely before frosting.

Cream Cheese Frosting

1. In a stand mixer or using a hand held mixer, whip cream cheese until soft and fluffy
2. Add icing sugar and vanilla, mix until well combined. Frost cake and serve.