Heat the oven to 350°F. Meanwhile, cut 1 medium green cabbage in half through the core. Cut each half into 4 wedges, keeping the core intact. If any outer leaves fall off, reserve them.

Heat 2 tablespoons of the olive oil in a 12-inch oven-safe skillet over medium-high heat until shimmering. Add half of the cabbage wedges cut-side down and add any loose leaves. Cook until charred in spots on 2 sides, about 3 minutes per side; transfer any loose leaves to a plate if they are ready before the wedges. Transfer the cabbage to the same plate.

Add 2 tablespoons of the olive oil to the skillet and repeat searing the remaining cabbage wedges; transfer to the plate.

Reduce the heat to medium and add the remaining 1 tablespoon olive oil to the skillet. Add ½ cup chopped sun-dried tomatoes and 1 tablespoon minced garlic. Cook, stirring constantly, until the garlic is fragrant and lightly toasted, about 30 seconds.

Add 1 ¾ cups low-sodium chicken broth, ½ cup heavy cream, 4 ounces cubed cream cheese, 1 ½ ounces finely grated Parmesan cheese, 1 tablespoon tomato paste, and 1 teaspoon Italian seasoning. Bring to a gentle boil over medium heat, whisking until the cream cheese is fully melted and the sauce is smooth and combined.

Season the cabbage with ¾ teaspoon kosher salt. Return the cabbage to the skillet in an even layer (they can overlap slightly), nestling it into the sauce.

Transfer the skillet to the oven. Bake, flipping the cabbage halfway through, until the sauce is thickened and the cabbage is very tender, 50 to 55 minutes total. Garnish with chopped fresh basil leaves and more grated Parmesan if desired.