Cut cabbage in quarters, lengthwise. Remove and discard core and slice as finely as possible across width. Place in large bowl.
Remove wispy fennel leaves. Chop and reserve for garnish. Cut bulbs in half and slice as finely as possible across width, discarding hard cores. Place in bowl with cabbage.
Combine remaining ingredients in another bowl. Add, half a cup at a time, to cabbage and fennel just until well moistened. You don't want a pool of dressing at bottom of bowl. Toss well and store in refrigerator.
c.1997, M.S. Milliken & S. Feniger, all rights reserved