Be sure to use a very sharp knife to get the best cuts on these firm winter veggies.
Peel away the loose outer leaves of the purple cabbage. Cut the head in half and cut out the core.
With the cut side of the cabbage down on the cutting board, make thin slices down through the cabbage to cut it into long shreds. Place the shredded cabbage into a very large bowl.
Slice the ends off the kohlrabi and use a vegetable peeler or sharp paring knife to peel them. Cut each bulb in half.
Lay them cut side down on the cutting board and slice into thin slices. Make a stack of 2-3 slices and cut them lengthwise into matchstick-sized pieces. Add them to the bowl.
Peel the carrots and cut the tops and tips from them. Slice the carrots in half lengthwise.
Lay them cut side down and slice them lengthwise into long planks. Make a stack of 2-3 planks and cut them lengthwise into matchstick-sized pieces. Add them to the bowl with the cabbage and kohlrabi.
Cut off the ends of the celery root and use the vegetable peeler to peel the skin away. Cut the celery root into matchstick-sized pieces following the same method as above for the carrots and kohlrabi.
Add the celery root to the bowl. Toss everything in the bowl together until the different veggies are well mixed.
Cut off and discard the ragged tips, white ends, and thicker light-green parts of the scallions. Pull the tip of your knife down the length of the remaining scallion to slice it lengthwise: continue to make these cuts to create long, sometimes curling strands of scallions. Set these aside.