Using a vegetable peeler, shave squash into ribbons to measure 5 cups. Discard seeds and core of squash.
Heat oil in a large nonstick skillet over medium heat. Add squash, onion, and garlic; cook 4 minutes or until onion is tender, gently stirring occasionally. Remove from heat. Add salt, red pepper, and black pepper, and toss gently to combine. Sprinkle with cheese.