Cut off stalks from fennel; reserve tops and discard stalks. Discard any wilted outer layers from fennel and cut a thin slice from base of bulb. Quarter fennel bulb lengthwise; slice very thinly. Set aside. Chop enough of the reserved fennel tops to make 1 tablespoon; set aside along with a few sprigs of the feathery leaves.
For vinaigrette, in a small screw-top jar combine the 1 tablespoon chopped fennel tops, the oil, vinegar, mustard, sugar, salt, and pepper. Cover and shake well.
In a very large serving bowl combine sliced fennel, cabbage, and zucchini; toss gently to combine. Pour vinaigrette over cabbage mixture; toss gently to coat. Cover and chill for 2 to 24 hours.
To serve, garnish the slaw with the reserved sprigs of feathery leaves.