Spiralize zucchini into noodles. Use julienne peeler if no spiralizer.
Pat zucchini noodles dry with paper towels to remove moisture.
Whisk olive oil, balsamic vinegar, honey, garlic, Italian seasoning, salt, and pepper. Set aside.
Heat 1 tablespoon olive oil in large skillet over medium heat.
Add garlic. Cook 30 seconds until fragrant.
Add zucchini noodles, salt, and pepper. Toss gently.
Cook 2 to 3 minutes, tossing frequently, until tender-crisp. Do not overcook.
Remove from heat. Transfer to serving bowls.
Top with cherry tomatoes, mozzarella, and basil.
Drizzle balsamic dressing over each bowl.
Sprinkle with Parmesan if using.
Serve immediately while warm.