Bring a large pot of salted water to a rolling boil. Add pasta and cook for 8-10 minutes, then drain and rinse under cold water.

In a medium mixing bowl, whisk together lemon zest, lemon juice, white balsamic vinegar, and Dijon mustard. Gradually add olive oil while whisking to emulsify. Fold in walnuts, capers, salt, and pepper.

Add cooled pasta to the dressing mixture and gently toss to coat.

Gently fold in arugula and basil leaves, being careful not to bruise the arugula.

Serve on a platter, topping with additional cheese and walnuts if desired. Best enjoyed immediately.