In a mixing bowl, combine cabbage, vinegar, lime zest, lime juice, and diced pepper.
Toss the mixture and let it marinate for at least 30 minutes.
When ready to prepare the slaw, sauté onions in a pan over medium heat for 3 minutes.
Add garlic to the onions and sauté until fragrant.
Stir in brown sugar and butter, allowing them to melt.
Add the marinated cabbage mixture to the pan.
Season with black pepper and mix while cooking to achieve the desired texture (preferably crispy).
After a few minutes, taste for texture and seasoning.
Transfer the slaw to a serving bowl and let it cool slightly.
Mix in apple, cilantro, and mint, and adjust seasoning to taste.
Serve immediately.