Toast the walnuts in a dry skillet over medium heat for 3-4 minutes, stirring frequently, until fragrant and golden—this deepens their nuttiness significantly. Once cooled slightly, chop them into 1/4-inch pieces and set aside. While the walnuts cool, zest and juice the lemons, tear the basil leaves by hand into 1/2-inch pieces (tearing rather than cutting prevents bruising and preserves delicate oils), halve the cherry tomatoes, and grate the parmesan cheese. Having all components ready ensures the assembly flows smoothly once the pasta is cooked.
Bring a large pot of salted water to a rolling boil and add the pasta. Cook according to package directions until al dente—I always use Barilla Penne for its reliable texture and ability to hold the dressing beautifully. Drain the pasta well but do not rinse it; the residual starch helps the dressing cling to each piece. Set aside to cool slightly while you prepare the dressing.
In a large mixing bowl, combine the lemon juice and zest, white balsamic vinegar, Dijon mustard, capers, caper brine, honey, salt, and black pepper. Whisk these ingredients together to emulsify slightly, then slowly drizzle in the olive oil while whisking constantly—I prefer Lucini Premium Select for its peppery finish that complements the bright lemon. This technique creates a more cohesive dressing that will coat the pasta evenly. Stir in the grated parmesan and toasted walnuts until well combined.
Add the cooked pasta from Step 2 to the vinaigrette in the bowl and toss thoroughly, ensuring every strand is coated with dressing and the flavors begin to meld. Add the halved cherry tomatoes and the hand-torn basil from Step 1, then toss gently to combine. Finally, add the arugula last—tossing it in at the end prevents it from becoming over-coated and wilted from the warm pasta, preserving its fresh peppery bite and texture. Serve immediately or let sit for 10-15 minutes for flavors to further develop.