Bring a large pot of salted water to a boil. Cook pasta until slightly softer than al dente. Drain and rinse under cold water to stop cooking.
In a large mixing bowl, whisk together lemon juice, zest, white balsamic vinegar, dijon mustard, capers (and brine), walnuts, salt, and pepper.
Slowly drizzle in the olive oil while whisking until emulsified. Stir in grated parmesan cheese.
Add the rinsed, cooled pasta to the bowl and toss until fully coated in dressing.
Add arugula and optional basil, then toss again gently to combine.
Serve immediately, or chill in the refrigerator until ready to serve.