Preheat the oven to 400 degrees F. Spray two baking sheets with nonstick cooking spray.
Place the flat side of the cabbage on your cutting board. Slice head of cabbage into 1-inch thick rounds. You should get about 4 to 6 slices, depending on the size of the cabbage.
Transfer cabbage steaks to the prepared baking sheets. Brush both sides of the cabbage with avocado oil then season both sides with salt and pepper.
Roast in the oven for 20 minutes. Sprinkle parmesan cheese over the top of each cabbage. Place back in the oven and roast for another 15 minutes, or until tender in the middle and golden brown on the outside.