1. Cook orzo according to package directions. When 3 minutes of cooking time remain, add asparagus. Cook for 1 minute, then add peas and cook for the final 2 minutes. Drain.
2. Meanwhile, use a vegetable peeler to make 12 curls of Parmesan. Grate remaining cheese and set aside.
3. Combine salt, lemon juice, and olive oil; whisk together. Toss orzo in lemon-juice mixture; stir in grated cheese and basil. Serve warm or at room temperature with Parmesan curls. Garnish with additional basil leaves, if desired.