Toast the 1/3 cup walnuts in a dry skillet over medium heat for 4 to 5 minutes, stirring frequently, until fragrant and darkened. Tip onto a plate to cool.

Trim and slice the 6 celery stalks on a diagonal to 1/4 inch thick. Soak in ice-cold water for 5 minutes, then drain and pat completely dry.

Whisk together the 3 tbsp olive oil, 2 tbsp lemon juice, 1 tsp lemon zest, 1 tsp Dijon mustard, 1/2 tsp honey, grated garlic, 1/4 tsp kosher salt, and 1/4 tsp black pepper until the dressing is cohesive and slightly thickened.

Toss the dried celery with the dressing, fold in the 1/4 cup parsley and cooled walnuts, transfer to a serving plate or shallow bowl, and scatter the 1/3 cup shaved Parmesan on top with a final grind of black pepper.