thinly slice the cabbage in a food processor using a 4 mm slicing disc or by hand. You should have about six packed cups. Put the cabbage in a large bowl. If using a food processor, switch to the grating disc and grated carrot and celery root or cut into very thin julienne strips by hand. You should have about 2 1/2 cups total. Add the carrot and celery root to the cabbage, along with the onion and 1 tablespoon salt and toss. Packed with slotted into a colander. Lay a plate that fits inside a colander on top of the slot and set a heady can or jar on top of the plate. Drain this in the sink over a bowl for two hours.
Coarsely chop the garlic. Sprinkle the garlic with a large pinch of salt and mash into a paste on a cutting board with the side of a chef's knife. In a small bowl, mix the mashed garlic, buttermilk, olive oil, lemon juice, chives, parsley, celery seeds, and 1/8 teaspoon pepper. Turn the slaw out onto a clean dish towel or some paper towels and pat thoroughly dry. Transfer the slaw to a large bowl, toss with the buttermilk dressing and season to taste with salt, pepper, and lemon juice if needed. Makes 5 to 6 cups or serves 6 to 8.