Grate the zucchini using the large holes of the grater. Do not squeeze the extra water out, simply transfer them in a bowl.
In a skillet add the olive oil and the garlic. Cook at medium heat for 1 min. Add the grated zucchini, adjust with salt and cook stirring for 4-5 min. Turn the heat off and let cool down for 5 minutes.
Transfer the zucchini in a bowl and add breadcrumbs, egg, mozzarella, Parmesan cheese and basil leaves. Mix well.
With your hands create small balls with 1 tablespoon of the zucchini mix. In a bowl add 1/2 cup of breadcrumbs and coat the zucchini balls. Place them on a baking sheet lined with parchment paper. Use all the zucchini mix. You should obtain 16 zucchini balls.
Refrigerate for 30 minutes. Remove from the fridge and drizzle 3 Tbsp of olive oil on top and bake in preheated oven to 400F for 15 min. Add 5 extra minutes in broil or grill mode. Remove from the oven, let the zucchini ball cool down for 5 min and serve warm.