Cut the cabbage into 8 wedges by slicing through the core so each wedge stays intact.
Heat ½ Tbsp olive oil in a large skillet over medium heat. Add the cabbage wedges cut-side down and sear 2–3 minutes per side until golden, working in batches if needed.
Transfer the seared wedges to a large baking dish, arranging them snugly in a single layer.
In the same skillet over medium heat, melt the butter. Add the shallot and garlic and cook until softened and fragrant, about 1 minute.
Pour in the chicken broth, scraping up the browned bits. Stir in the heavy cream, parmesan, chili oil, oregano, salt and black pepper. Simmer 3–4 minutes until smooth and slightly thickened.
Preheat the oven to 350°F. Pour the sauce evenly over the cabbage and bake 50–60 minutes until the cabbage is tender and the top is lightly golden.
Garnish with chopped parsley and extra parmesan before serving.