1. Shave zucchini and yellow squash into ribbons using a vegetable peeler, stopping at the seeds; place ribbons in a large bowl. Discard seed cores.
2. Combine oil, rind, juice, salt, pepper, and garlic in a small bowl; stir with a whisk. Drizzle oil mixture over vegetable ribbons; sprinkle with basil and oregano. Toss gently. Sprinkle with cheese. Serve immediately.