Preheat the oven to 180 °C. Line a cake tin with baking paper.
Combine wet ingredients
In a large bowl combine 2 egg, ½ cup applesauce, ¼ cup olive oil, ⅔ cup milk, 2 tsp vanilla extract, and ⅓ cup maple syrup.
Combine dry ingredients
In a separate large bowl combine 2 cups flour, 2 tbsp baking powder, 1 tsp baking soda, 2 tsp cinnamon, ¼ tsp ground ginger, ½ tsp nutmeg, and ¼ tsp sea salt.
Combine mixtures
Peel and grate 2 carrot. Roughly chop ½ cup walnuts. Add the dry ingredients to the bowl with the wet ingredients. Mix until just combined, being careful not to over-mix. Then carefully stir in the carrots and walnuts. Pour the batter into the prepared cake tin.
Bake cake
Bake for 35-40 minutes or until a toothpick inserted in the middle comes out clean. Let it cool in the tin for 10 minutes. Then lift the cake out with baking paper and place it on a cooling rack to cool completely.
Ice cake
Once the cake is cooled, ice it with your favourite icing. Slice and enjoy! Keep leftovers in the fridge.