Preheat oven to 425°F. Cut cabbage into 8 wedges (about 1 inch wide), keeping the core intact.

Combine Parmesan, garlic, oil, vinegar, soy sauce, and salt in a small bowl. Arrange the cabbage wedges, cut-side down, on a large rimmed baking sheet. Brush all sides of the cabbage with the garlic-Parmesan mixture. Roast until the edges are golden brown, about 20 minutes. Flip and roast until the cabbage is tender and golden, about 10 minutes more. Garnish with crushed red pepper and/or Parmesan, if desired.