Preheat oven to 350°F.

Slice cabbage in half through the root. Cut each half into 4 (about 2-inch-thick) wedges, keeping core intact.

Heat 1 tablespoon sun-dried tomato oil in a large, enamel-coated cast-iron or stainless-steel skillet over medium-high heat.

Add 4 cabbage wedges; cook until deeply browned on both sides, 3 to 4 minutes per side; transfer to a large rimmed baking sheet.

Repeat with 1 tablespoon oil and the remaining 4 cabbage wedges. Do not wipe the skillet clean.

Add ½ cup sun-dried tomatoes, 2¼ cups broth, ¼ cup cream, 1 tablespoon tomato paste, 1½ teaspoons Italian seasoning, ¼ teaspoon crushed red pepper, the minced garlic, the softened cream cheese, ¼ teaspoon salt and the remaining 1 tablespoon oil to the skillet; cook over medium heat, whisking constantly, until well combined and boiling, about 2 minutes.

Stir 2 teaspoons cornstarch and 2 teaspoons water together in a small bowl until fully combined. Whisk into the mixture in the skillet; remove from heat.

Whisk in ½ cup Parmesan until melted, about 1 minute.

Sprinkle the tops of the cabbage wedges with ¼ teaspoon pepper and the remaining ¼ teaspoon salt; nestle the wedges into the skillet, overlapping just slightly if needed to fit in a single layer.

Bake until the cabbage is fork-tender and the sauce has slightly thickened, 50 minutes to 1 hour, flipping the cabbage halfway through.

Sprinkle the cabbage with the remaining 1 tablespoon Parmesan. Garnish with basil, if desired.