Broccoli: slice off all the broccoli florets first, and either reserve them for another recipe or give them a quick blanch: toss in boiling salted water for 3-4 minutes and then ice water for 3-4 minutes. Add them in before dressing. Slice off a circle of the bottom of the stalk and discard. Peel off the thick, light green skin on the stalk, and then use a julienne peeler, a box grater or the grating blade on your food processor to turn into shreds. Taste one-- they're sweet, almost like apples!
Cabbage: Slice in half, through the core, and then in half again through the core to have 4 identical wedges. Cut out the thick white core and discard it. You'll only need to shred ~ one wedge, so save the rest for another use.
Kale: Slice out and discard the center, tough rib by stacking the leaves and cutting it out in an upside down V. Roll the leaves up to form a long cylinder. Slice thinly.
Carrots: Scrub and peel the carrots first (you'll need about 2.)
Onion: Cut in half through the stem end. Set the flat side on the the cutting board and slice into thin semi-circles. If you want to take out some of the bite, soak in cold water for 5-10 minutes.
Mix all the ingredients into a bowl except for the oil(s). Slowly drizzle in the oil, whisking, to pull it together. Alternatively, add all the ingredients to a mason jar with a lid and shake, shake, shake!