Cut the half head of cabbage through the core into 4 thick wedges, leaving part of the core attached to each piece.
Pat the cabbage dry if needed.
In a large bowl, combine the olive oil, minced garlic, salt, black pepper, Italian seasoning, and Parmesan.
Coat each cabbage wedge thoroughly in the seasoning mixture, working some seasoning between the outer leaves.
Preheat the air fryer to 375°F (190°C) if needed for your model.
Arrange the cabbage wedges in the air fryer basket in a single layer without overcrowding.
Air fry for 15–18 minutes, carefully turning the wedges halfway through.
Continue cooking until the center is tender and the outer leaves are browned and lightly crisp.
Remove carefully and serve immediately.