Preheat the oven to 170 degrees Celsius/ 340 degrees Fahrenheit. Line a brownie pan (20x20 cm/ 8x8 inches) with baking paper.
Place the butter and the chopped chocolate in a small saucepan and heat gently until melted. Do not let come to a boil. Leave to cool for a few minutes while preparing the rest.
Grate the zucchini and squeeze them in your hand to remove the extra moisture. Roughly chop the cashews.
Whisk the eggs, sugar, and vanilla sugar with a hand-held mixer until frothy.
Mix the flour, cocoa, and baking powder together and add to the egg mixture. Incorporate and add the butter chocolate mixture. Fold in the zucchini, cashew nuts, and half of the chocolate chips.
Pour this mixture into the prepared pan and sprinkle with the remaining chocolate chips. Bake for 30 to 35 minutes, depending on your oven.
Check by inserting a toothpick in the middle of the cake. It should come out still a little moist. Leave the zucchini chocolate brownies cool in the pan, take out, and dust with icing sugar if desired.
The zucchini brownies keep well in an airtight container for several days.