Preheat the oven to 350 degrees F (175 degrees C). Grease a large, rimmed baking sheet with butter. Combine flour, coconut, baking powder, and salt in a bowl. Combine butter, sugar, and vanilla sugar in a large bowl; beat with an electric mixer until very smooth and creamy, about 5 minutes. Add eggs one at a time, and beating well after each addition. Fold in zucchini and carrots. Stir in flour mixture alternately with milk until batter is well combined. Spread onto the prepared baking sheet. Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 45 minutes. Pour orange juice over warm cake immediately after removing from the oven, so it can soak up the liquid.