Preheat oven to 350°F. Slice cabbage in half through the stem end. Cut each half into 4 (2-inch) 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 ⅛ teaspoon each salt and pepper. Repeat with 1 tablespoon oil, the remaining cabbage wedges and ⅛ teaspoon each salt and pepper.

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, overlapping them if necessary. 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 ½ cup Parmesan. Garnish with parsley, if desired.