Into a small mixing bowl, measure the mayonnaise, lime juice, chili powder, salt and ground black pepper; whisk until well combined; set aside.
Use a vegetable peeler to shred the cabbage into long thin strands; a food processor or a box grater can also be used to shred the cabbage; place the cabbage into a large mixing bowl.
Thinly chop the green onions and finely chop the jalapeño; add both to the bowl with the cabbage.
Chop the parsley or cilantro, if using, and add to the bowl.
Regardless if using canned corn, frozen corn or cooked fresh corn, be sure to drain well; if your corn is wet, it will dilute the dressing; add the corn to the bowl.
Add in the cheese.
Finally, whisk the dressing mixture again, ensuring that nothing has settled to the bottom.
Pour this mixture over the vegetables and toss well, with tongs, until thoroughly mixed.
Transfer to a food-safe container with a tight-fitting lid and refrigerate for at least two hours.
Before serving, toss one more time.
