Using a vegetable peeler, peel the zucchini lengthwise into thin ribbons; discard the seedy centers. Transfer to a bowl. Using a mandoline, shave the fennel bulb into pieces; discard the core. Toss with the zucchini. Fold in the avocado and parmesan. Sprinkle with the lemon zest, then cover and refrigerate until ready to serve.
In a small bowl, combine the EVOO, vinegar, mustard, 1/8 tsp. coarse salt and 1 pinch pepper. Drizzle the dressing over the salad; toss gently.
How To Make Zucchini Ribbons