Toast the walnuts in a dry skillet over medium heat for 3-4 minutes until fragrant and slightly golden, then chop them roughly.

Zest and juice the lemons in a small bowl. Tear the basil leaves into bite-sized pieces, halve the cherry tomatoes, and grate the parmesan cheese.

Bring a large pot of salted water to a boil. Cook the pasta until al dente, about 8-10 minutes. Drain and rinse under cold water.

In a large mixing bowl, combine lemon juice, zest, white balsamic vinegar, Dijon mustard, capers, honey, salt, and black pepper. Whisk in the olive oil until emulsified.

Add the toasted walnuts and grated parmesan to the dressing, mixing gently. Then add the cooled pasta, tossing to coat evenly.

Fold in the halved cherry tomatoes and basil. Add the arugula just before serving for freshness.