Preheat your grill or a grill pan on the stovetop to medium heat.
Mix the ground turkey, grated zucchini and onion, bread crumbs salt, pepper, garlic powder, and oregano together in a large mixing bowl until evenly combined.
Divide the turkey mixture into eight equal portions and then form them into patties.
Place the burger patties on the hot grill and cook for 10-12 minutes over direct heat, flipping once. When the burgers have about 3 minutes left, place 1-2 slices of mozzarella on each patty so that the top is covered. Once the burgers reach an internal temperature of 165 degrees F and the cheese has melted, they're ready. (see note)
Take the burgers off the grill. Place a burger patty onto a bottom burger bun. Top with a tomato slice and some fresh basil. Drizzle with balsamic glaze if desired. Add the top bun and any condiments you like before serving warm.
Notes
If you're cooking over charcoal, the cooking time will vary. Once it's easy to get the spatula under the burger patty without scraping and the liquids begin to pool on top, it's ready to flip.