Pat the pork shoulder dry with paper towels and generously coat all sides with brown sugar, smoked paprika, garlic powder, dry mustard, black pepper, and salt.

Pour the apple cider and white wine into the bottom of the slow cooker, then place the seasoned pork on top. Cover and cook on low for 7 hours, or until the meat is fork-tender.

Remove the pork to a cutting board and let it rest for 10 minutes before shredding it with two forks into bite-sized pieces; reserve the cooking liquid for later if you need to moisten the meat.

In a large bowl, whisk together mayonnaise, apple cider vinegar, yellow mustard, and sugar until smooth, then fold in the shredded green and purple cabbage until evenly coated.

Toss the thinly sliced apples with cornstarch and a pinch of salt, then fry in a small amount of olive oil over medium heat until golden and crisp, about 3–4 minutes per batch.

Transfer the shredded pork back to the slow cooker or a serving bowl, spoon some of the reserved cooking liquid over it if needed, and serve alongside the creamy coleslaw and crispy apple slaw.

Before serving, verify that the pork is cooked through by checking the internal temperature with a food thermometer to ensure it meets your local safety guidelines.