Preheat oven to 375°F (190°C).
Cut the cabbage into 8 wedges, keeping the core intact on each wedge.
Heat olive oil in the cast iron skillet over medium-high heat and sear cabbage wedges 2 to 3 minutes per side until golden. Work in batches if needed.
Transfer seared wedges to a plate and season with salt and pepper.
Reduce heat to medium, add butter, and cook red onion for 2 to 3 minutes until softened.
Add garlic and cook for 30 seconds until fragrant.
Pour in chicken broth to deglaze the pan, scraping up browned bits.
Add cream cheese and whisk until melted and smooth.
Stir in heavy cream, sun-dried tomatoes, oregano, thyme, rosemary, salt, pepper, and red pepper flakes if using. Simmer for 2 to 3 minutes to slightly thicken the sauce.
Remove from heat and stir in Parmesan cheese until fully melted and incorporated.
Nestle the cabbage wedges back into the skillet and spoon sauce over the tops.
Cover with foil or lid and bake for 45 minutes.
Uncover, baste cabbage with sauce, and bake another 15 to 20 minutes until fork-tender.
Let rest 5 minutes before serving. Garnish with chopped parsley and extra Parmesan.