Arrange the thinly sliced zucchini on a kitchen towel and season with a pinch of salt. Leave them aside for about one hour, so thy will lose a bit of liquid that could make the cake too wet.
Heat oven to 170°C.
Whisk the eggs with the sugar, milk, olive oil, flour and vanilla seeds, then add gently the zucchini and the trimmed basil leaves.
Grease a 25 x 40 cm baking tin with olive oil and scoop the batter inside.
Bake for about 45- 50 minutes until golden.
Let it cool down and serve dusted with icing sugar.