Use a mandoline or a sharp knife to thinly slice the cabbage. For a very fine grate, use the large holes on a box grater. Use a box grater on the carrots, or use store-bought shredded carrots.
In a large bowl, whisk together the mayo, mustard, vinegar, lemon juice, onion powder, celery seeds, and maple syrup. Season to taste with salt and pepper as needed.
Add the cabbage, carrots, jalapeno and parsley if using. Toss to combine. Taste, adding more mayo for richness, more lemon juice or vinegar for tang, and salt/pepper to taste.