Trim stalks and any discolored areas from fennel bulb. Cut bulb in half lengthwise, lay a flat side on a work surface, and cut into very thin slices. Repeat with other half and set slices aside.
Cut pear into quarters and scoop out cores. Peel quarters and cut into 1/4-in. slices. Set aside.
Whisk together walnut oil, lemon juice, and salt in a small bowl. Taste and add more salt if you like.
Arrange fennel slices and pear slices on 4 salad plates. Drizzle each plate with 1 tbsp. dressing. Arrange walnuts and parmesan on top. Serve immediately.
Note: Nutritional analysis is per serving.