Preheat the oven to 425 degrees F. Grease a large baking sheet with oil.
Cut the mozzarella into 12 equal sized square pieces and set aside.
Shred zucchinis using a food processor or hand cheese grater. Use a clean kitchen towel to wrap up the shredded zucchini and squeeze as much liquid as you can out of it (and discard).
In a large bowl mix together the shredded zucchini, eggs, breadcrumbs, Parmesan, basil, garlic, and salt until well combined.
It's time to form the "meatballs." Take a handful of the zucchini mixture, shove one of the mozzarella squares in the middle, then form it into a "meatball" with the mozzarella completely covered on the inside. Squeeze the "meatball" together tightly and discard any additional excess liquid. Repeat with remaining ingredients and place on the greased baking sheet.
Bake for 14 to 16 minutes or until golden brown on the bottom. Serve warm over noodles with red sauce and (if desired) garnish with additional Parmesan cheese. Enjoy!