Shred the cabbage into thin 1/8-inch strips using a sharp knife or mandoline, then transfer to a large mixing bowl. Grate the carrot using the large holes of a box grater and mince the onion finely. Add both to the bowl with the cabbage. I find that shredding everything by hand rather than using a food processor helps maintain a better texture—the vegetables stay crisp instead of becoming too wet.

In a separate small bowl, whisk together the vegan mayonnaise, lemon juice, and cider vinegar until smooth and well combined. Add the sugar, salt, pepper, and celery seed, then whisk again until the dressing is uniform and all the sugar has dissolved. This creates a balanced, creamy dressing base with bright acidity and subtle spice.

Pour the dressing from Step 2 over the vegetables from Step 1 and toss well until every piece is evenly coated. Let the coleslaw sit at room temperature for 20-60 minutes before serving, tossing occasionally—the longer it sits, the more the flavors meld and the cabbage becomes slightly tender while maintaining its crunch. I prefer to let mine rest for at least 30 minutes to allow the vegetables to soften slightly and absorb the dressing's flavors.