Step 1: Heat the Oven and Prepare the Zucchini - Preheat your oven to 400°F so it is fully heated by the time the meatballs are shaped. Shred the zucchini, then gather it in your hands or a clean kitchen towel and gently squeeze out the obvious excess liquid. You do not need to wring every drop from it. The goal is simply to keep the meatball mixture from becoming watery while leaving enough moisture behind to help keep the chicken tender.
Step 2: Mix the Chicken Meatball Mixture - Add the ground chicken to a large bowl along with the squeezed zucchini, breadcrumbs, mozzarella, 1/2 cup ricotta, salt, black pepper, minced garlic, and egg. Use clean hands to gently combine everything until the ingredients are evenly distributed. Try not to squeeze and knead the mixture more than necessary. Ground chicken becomes firmer when it is worked aggressively, so stop mixing once you no longer see obvious streaks of egg, cheese, or breadcrumbs.
Step 3: Shape the Meatballs Evenly - Lightly dampen your hands with water before you start shaping because the chicken mixture will be soft and a little sticky. A number 20 scoop is useful for making evenly sized portions, but an ordinary spoon works just fine if that is what you have. Scoop the mixture and gently roll each portion into a ball. Aim for roughly 24 meatballs. Keeping them similar in size helps every meatball finish cooking at about the same time.
Step 4: Arrange and Bake the Meatballs - Pour the olive oil into the bottom of a casserole dish and spread it around so the surface is lightly coated. Arrange the meatballs in the dish with a little room between them, then place the dish in the preheated oven. Bake for 20 minutes. At this stage you are giving the meatballs time to set, cook through most of the way, and develop a little golden color before adding the marinara.
Step 5: Add the Marinara and Cheeses - Carefully remove the hot casserole dish from the oven. Pour the marinara around and over the meatballs, making sure some sauce settles between them where it can bubble and thicken. Sprinkle the Parmesan across the top, add a few torn or whole basil leaves, then tuck small spoonfuls of the additional ricotta between the meatballs. Do not worry about making it look too neat. Those little pockets of ricotta are especially good once they warm into the sauce.
Step 6: Finish Baking Until Bubbling - Return the casserole dish to the oven and bake for another 10 minutes. The marinara should be hot and bubbling around the edges, the Parmesan should be melted, and the tops of the meatballs should have a little golden color. For food safety, check one of the larger meatballs with an instant read thermometer and make sure the center has reached 165°F.
Step 7: Garnish and Bring It to the Table - Take the casserole out of the oven and scatter fresh basil over the top just before serving. I like to let it sit for a few minutes because the sauce settles slightly and nobody at the table burns their mouth on molten cheese, which is the sort of lesson most families only need to learn once. Spoon the meatballs and plenty of marinara over pasta, rice, or mashed potatoes, and make sure every plate gets a little of that warm ricotta from the top.