Begin by preparing the cabbage. Slice the green cabbage into 8-10 wedges, leaving the core intact.
Thinly slice the Fontina cheese into 1/8 inch slices. Cut the Soppresata slices in half.
Working with one cabbage wedge at a time, gently pull back individual layers, inserting one Fontina cheese slice, followed by one Soppresata slice, then one sage leaf, tearing any large sage leaves in half. Continue this process until all cabbage layers are stuffed. Each wedge should have 3-4 cheese slices, 3-4 Soppresatta slices, and 3-4 sage leaves.
Lightly coat finished wedges with 1 tbsp olive oil, 1 tsp salt, and 1 tsp black pepper.
Line the air fryer basket with a piece of parchment paper. Air Fry cabbage wedges at 385°F for 15-17 Minutes, or until charred and crispy at the edges.
Plate each dish with 2-3 cabbage saltimbocca wedges. Drizzle with white balsamic and shaved Parmesan. Sprinkle salt and pepper to taste.