Preheat the air fryer to 400F for 5 minutes.
While the air fryer is preheating, prepare the cabbage. To a large mixing bowl, add the cabbage, olive oil, apple cider vinegar, garlic powder, salt, and pepper. Mix until the cabbage is evenly coated in the oil and seasonings.
Transfer half of the cabbage to the air fryer and cook for 5 minutes. Stir, and cook for 5 more minutes. Stir one more time, and cook for an additional 3-5 minutes, depending on how tender you like it. Repeat with the second half of the cabbage. (See notes if you want to cook the cabbage all at once instead of in two rounds.)*
While the second half of the cabbage is cooking, prepare the optional balsamic glaze (if using). To a small saucepan, add the balsamic vinegar and honey. Whisk together. Heat over medium to medium-low heat, and bring to a simmer. Simmer for about 7 minutes, or until it reduces by half and becomes syrupy.**
Transfer the cabbage to a serving dish and drizzle half of the glaze over it. Gently toss the cabbage to evenly coat it in the glaze, drizzle the remaining half on top, and serve.