If you would prefer to shred the broccoli stems yourself instead of using a mix: 1. Trim the broccoli: Cut off the florets from the broccoli head, leaving behind the thick stems. 2. Peel the stems: Use a vegetable peeler or a paring knife to remove the tough outer layer of the broccoli stems. This outer layer can be fibrous and may not be as pleasant to eat in the slaw. 3. Prepare the stems: Take the peeled broccoli stems and shred them using either a box grater or a food processor with a grating attachment.