Preheat oven to 425°F with racks in top third and lower third positions. Toss chopped cabbage with 2 tablespoons oil in a large bowl until well coated. Transfer the cabbage to 2 large rimmed baking sheets; spread in an even layer.
Roast until the cabbage is tender and golden in spots, about 25 minutes, rotating the pans between the top and bottom racks halfway through.
Meanwhile, whisk ¼ cup Parmesan, 3 tablespoons lemon juice, 2 tablespoons shallot, 1 teaspoon mustard, ½ teaspoon oregano, ¼ teaspoon salt, ¼ teaspoon pepper and the remaining 3 tablespoons oil together in a large bowl.
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. Top with 2 tablespoons walnuts before serving. Garnish with additional pepper, if desired.
