Preheat oven to 180 C degrees. Oil and line large cake pan.
Coarsely grate courgettes/zucchinis and squeeze dry in towel.
Blend avocado with oil until smooth.
Mix courgette/zucchini with avocado, oil, two limes zested and juiced, vanilla, sugar, and eggs.
Add flour, baking powder and turmeric.
Bake in cake pan for 15-20 minutes or until knife in center comes out clean.
Let cool while you make the icing.
Sift the icing sugar/ powedered sugar in a bowl, squeeze the third lime in and add milk. Add more sugar if you want it thicker or more lime juice if it's too thick.
Pour on top of cooled birthday cake and add lime zest on top of icing.