Toast the walnuts in a dry skillet over medium heat for 3-4 minutes, stirring frequently, until fragrant and golden. Let cool, then chop into ¼-inch pieces.

Zest and juice the lemons, tear the basil leaves, halve the cherry tomatoes, and grate the parmesan cheese.

Bring a large pot of salted water to a rolling boil. Cook pasta according to package directions until al dente. Drain well but do not rinse; set aside to cool slightly.

In a large mixing bowl, combine lemon juice and zest, white balsamic vinegar, Dijon mustard, capers, caper brine, honey, salt, and black pepper. Whisk together and slowly drizzle in olive oil while whisking constantly.

Stir in grated parmesan and toasted walnuts until well combined.

Add the cooked pasta to the dressing and toss thoroughly. Add halved cherry tomatoes and torn basil, then toss gently to combine. Add arugula last to prevent wilting.

Serve immediately or let sit for 10-15 minutes for flavors to develop.