1. Using a sharp knife, cut the cabbage in half through the stem end. Slice the cut face of each half into paper-thin slices. Place the sliced cabbage in a large bowl and add ice water to cover. Set aside.
2. Fill another large bowl with ice water and squeeze the juice of ½ lemon into it. Bring a large saucepan three-fourths full of water to a boil over high heat and add the juice of the remaining lemon half.
3. Cut off the stems and feathery fronds of the fennel bulbs and remove any bruised or discolored outer leaves. Working with 1 fennel bulb at a time, cut the bulb in half lengthwise and cut out any tough core parts. Using the small julienne blade of a mandoline, slice each half into matchsticks and place immediately in the bowl of lemon water. Repeat with the remaining fennel bulbs.
4. When all the fennel is cut, transfer with a slotted spoon to the boiling water and blanch for 30 seconds. (Reserve the bowl of water and lemon for the apples.) Drain the blanched fennel and rinse well under cold running water. Transfer to a fresh bowl of ice water. Set aside.
5. Working with 1 apple at a time, quarter it and cut away the core. Starting with the rounded side, slice each quarter into matchsticks on the mandoline and place immediately in the reserved lemon water. Repeat with the remaining apples.
6. In another bowl, combine the mayonnaise, sugar, lemon juice, vinegar, the 2 Tbs. milk and the salt and mix together. Taste. The dressing should be both sweet and tangy, and the consistency should be pourable, not thick. Add a little more milk if the dressing is too thick. Taste and adjust the seasonings.
7. Drain the cabbage, pat dry and place in a large bowl. Drain the fennel, squeeze gently to remove excess water, pat dry and add to the bowl of cabbage. Drain the apples, pat dry and add to the bowl. Add the raisins, green onions and parsley. Pour the dressing over all and mix well. Cover and refrigerate until ready to serve.