Position oven racks in top third and lower third; preheat to 425°F.
Toss cabbage with 2 tablespoons oil and salt in a large bowl until well coated. Spread in an even layer on 2 large rimmed baking sheets.
Roast the cabbage until tender and golden, about 25 minutes, rotating the pans between top and bottom racks halfway through.
Meanwhile, whisk Parmesan, vinegar, soy sauce, mustard, garlic, pepper and the remaining 2 tablespoons oil together in a large heatproof bowl. (For a creamier dressing, process in a blender until creamy and smooth, about 30 seconds.)
Transfer the hot roasted cabbage to the bowl with the dressing; toss until evenly coated. Let stand for 15 minutes to allow the flavors to meld. Garnish with additional pepper before serving, if desired.
