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Fit a food processor with the slicing blade. Cut the florets off of the broccoli, then feed them into the food processor to thinly slice them. Peel the stems of the broccoli and the carrots, then cut them into pieces to fit into the food processor. Change the blade to the grating blade and feed them through the food processor. Alternate method: Thinly slice the florets with a knife. Then use a box grater to large grate the peeled broccoli stems and carrots.
Place the sliced vegetables (or bags of broccoli slaw) into a large bowl. In a small bowl, mix together the mayonnaise, apple cider vinegar, sugar, dill, celery seed, kosher salt, and several grinds fresh ground pepper.
Add the dressing to the vegetables and stir until coated. If desired, stir in sunflower seeds or dried cranberries. Eat immediately or refrigerate up to 2 days.