Position oven rack in lower third; preheat to 425°F. Line a large rimmed baking sheet with foil. Remove and discard any loose outer leaves from cabbage; trim root end and slice the cabbage into 4 (1-inch-thick) steaks.
Whisk oil, vinegar, 1/4 teaspoon pepper and salt together in a small bowl. Brush the mixture evenly over both sides of the cabbage steaks; place them on the prepared baking sheet. Roast until browned on the bottom, about 25 minutes, rotating the pan from front to back halfway through.
Meanwhile, combine Parmesan, parsley, thyme, paprika, garlic powder and the remaining 1/4 teaspoon pepper in a small bowl; stir well.
Remove the baking sheet from the oven. Using a flexible metal spatula, carefully flip the cabbage steaks. Sprinkle the Parmesan mixture evenly over the tops of the steaks (about 2 tablespoons each).
Roast until the cabbage is tender and the cheese mixture is golden brown, 10 to 12 minutes, rotating the baking sheet from front to back halfway through.
Drizzle with balsamic glaze, if using, and garnish with additional parsley, if desired.