Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions until al dente. Drain and rinse under cold water to stop the cooking process.
Bring a large saucepan of salted water to a boil. Blanch the asparagus for 1-1 1/2 minutes or until tender-crisp. Drain in a colander, then transfer to an ice bath. Once completely cooled, drain again, and set aside.
In a small skillet, toast pine nuts on medium-low heat until lightly browned, stirring often. Watch closely as they can burn quickly.
In a small bowl, whisk together 1 tablespoon lemon zest, 1/3 cup lemon juice, olive oil, white wine vinegar, salt, and pepper until well combined.
In a large bowl, combine the cooked and cooled pasta, asparagus, fresh basil, pine nuts, and shaved Parmesan.
Pour the dressing over the salad and toss to coat evenly. Transfer to a serving bowl. If desired, garnish with extra Parmesan cheese, pine nut, basil, and/or lemon slices.