Toast the Walnuts: In a dry skillet over medium heat, add the walnuts and toast them for 3-4 minutes, stirring frequently until golden brown and fragrant. Remove from heat and let cool.

Prep Ingredients: Zest and juice the lemons, tear the basil, halve the cherry tomatoes, and grate the Parmesan.

Cook Pasta: In boiling salted water, cook pasta for about 8-10 minutes until al dente, then drain without rinsing.

Make Dressing: In a bowl, combine lemon juice and zest, vinegar, mustard, capers, brine, honey, salt, and pepper. Whisk and gradually drizzle in olive oil.

Combine Everything: In a large bowl, add pasta and dressing, then toss. Add cherry tomatoes and basil gently.

Add Arugula: Fold in arugula just before serving to keep it crisp.