Toast the walnuts: Place the chopped walnuts in a dry skillet over medium heat. Stir often until they smell nutty and darken slightly, about 4 minutes, then set aside to cool.
Make the vinaigrette: In a small bowl, whisk together the lemon zest, 2 tablespoons of lemon juice, olive oil, honey, salt and pepper. Whisk until the mixture looks slightly thickened and no longer separates.
Slice the apple: Cut the apple into thin wedges, leaving the skin on for color and texture. Slice it close to serving time so the edges stay crisp.
Toss apple in lemon juice: Place the apple slices in a bowl with the remaining tablespoon of lemon juice. Toss gently to coat, which keeps the slices from browning for up to an hour.
Arrange the arugula: Spread the dried arugula across a wide serving platter instead of piling it in a deep bowl. This helps the dressing reach every leaf evenly.
Add the toppings: Scatter the lemon-coated apple slices, toasted walnuts and shaved parmesan over the arugula. Distribute them evenly so every serving gets a bit of each.
Drizzle with dressing: Pour the vinaigrette over the salad in a thin stream, starting at the edges and working inward. Use just enough to coat the leaves lightly without pooling at the bottom.
Toss and serve: Toss gently with your hands or salad tongs until everything is coated and the leaves still stand tall. Serve right away while the apple is crisp and the greens are glossy.