Toast the walnuts. Preheat the oven to 350°F. Spread the walnuts on a sheet pan in one layer. When the oven is hot, bake until lightly toasted and fragrant, about 7 minutes. Remove and let cool.
Make the dressing. In a small bowl or pitcher, whisk together the olive oil, cream (if using), 1 ½ tablespoons of the lemon juice, and a pinch of salt and pepper. Taste and add more lemon juice, olive oil, or salt if needed.
Dress the salad. Place the fennel in a shallow serving bowl or deep plate. Add half of the cooled walnut pieces and half of the shaved parmesan. Just before serving, pour the dressing over and toss gently to thoroughly coat the fennel.
Finish and serve. In a small bowl, mix the chopped fennel fronds with the lemon zest and sprinkle over the salad. Garnish with the remaining walnut pieces and parmesan shavings and grind a touch more pepper on top. Let the salad rest just a minute or two before serving.
