Finely slice the cabbage; a mandolin slicer works great and shreds your cabbage really finely, but it can definitely be done by hand using a sharp chef's knife. Place cabbage in a salad bowl.
Cut avocado in half, use a spoon to scoop out the good stuff and discard the skin and pit. Dice avocado and place it over the cabbage.
Combine all dressing ingredients and pour over cabbage and avocado. Toss gently to coat.