Run zucchini and carrots through a spiralizer to create noodles, or cut long noodles with a julienne peeler or ribbons with a vegetable peeler. Place in a large bowl.
Working with 1 spear at a time, shave asparagus into ribbons with a vegetable peeler, stopping short of tips. Add shaved asparagus, tomatoes, peas, and green onion to bowl. Gently toss to combine.
In a separate smaller bowl, combine basil, oil, lemon juice, salt, and pepper. Stir with a whisk. Pour over salad and gently toss to combine. Divide into 3 bowls and top evenly with Parmesan cheese.
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