Remove upper stalks from fennel, including feathery leaves; reserve leaves and discard stalks. Discard any wilted outer layers on fennel bulbs; cut off a thin slice from base of each bulb. Quarter each fennel bulb lengthwise; slice very thinly. Set aside. Chop enough of the reserved fennel leaves to make 1 tablespoon; set aside along with a few sprigs of the feathery leaves.
In a small screw-top jar with a tight-fitting lid, combine the 1 tablespoon chopped fennel leaves, olive oil, vinegar, mustard, sugar, salt and black pepper. Cover and shake well. Set aside.
In a very large serving bowl, combine the sliced fennel, cabbage and zucchini. Pour the vinaigrette over cabbage mixture. Toss lightly to coat. Cover and chill for 2 to 24 hours.
To serve, garnish with reserved sprigs of feathery leaves.
Place salad in plastic container and chill in the refrigerator for up to 24 hours. Transport in an insulted cooler with ice packs.
A mandoline makes slicing the fennel simple.