Preheat oven to 350°F. Slice cabbage in half through the stem end. Cut each half into 4 wedges, keeping the stem and core intact. Heat 1 tablespoon oil in a large cast-iron or other heavy ovenproof skillet over medium-high heat. Add 4 cabbage wedges; cook until deeply browned on both sides, about 5 minutes per side. Transfer to a plate; sprinkle both sides evenly with salt and pepper. Repeat with remaining wedges.
Reduce heat to medium; add the remaining 2 tablespoons oil, 1 cup onion, sliced garlic, 1 teaspoon Italian seasoning and ¼ teaspoon crushed red pepper. Cook, stirring often, until the onion starts to soften and brown, 2 to 3 minutes. Add 2 ounces cream cheese; cook, stirring constantly, until melted and creamy, about 1 minute. Stir in 2 cups broth and the remaining ¼ teaspoon each salt and pepper; cook, stirring occasionally, until boiling.
Stir 2 teaspoons each cornstarch and water together in a small bowl until smooth; whisk into the mixture in the pan. Remove from heat; whisk in ½ cup Parmesan until melted.
Return the cabbage wedges to the pan; bake, turning once, until the cabbage is very soft and the sauce has reduced and thickened, about 50 minutes. Let stand for 5 minutes. Sprinkle the cabbage wedges with the remaining Parmesan. Garnish with parsley, if desired.
