Toast the Walnuts: Preheat oven to 350°F. Spread walnuts on a sheet pan and bake for 7 minutes until lightly toasted and fragrant. Let cool.
Prepare the Dressing: In a small bowl, whisk olive oil, cream (if using), 1 1/2 tablespoons lemon juice, salt, and pepper. Adjust seasoning as needed.
Dress the Salad Base: Place shaved fennel in a serving bowl or plate. Add half of the cooled walnuts and half of the shaved Parmesan.
Add Dressing: Pour the dressing over the fennel just before serving, tossing gently to coat.
Prepare Garnish: In a small bowl, mix chopped fennel fronds with lemon zest.
Finish the Salad: Sprinkle the fennel fronds mixture, remaining walnuts, and Parmesan over the salad.
Serve: Grind a bit of pepper on top and let rest briefly before serving.