Heat the butter and olive oil in a large skillet over medium-high heat. Add cabbage wedges, flat side down, and sear undisturbed for 3 to 4 minutes per side until golden brown. Use tongs to flip. Remove to a plate and set aside.
In the same skillet, lower the heat to medium. Add chopped onion and cook until soft and golden, about 5 minutes.
Stir in minced garlic and Cajun seasoning; cook for 1 minute until fragrant.
Pour in the heavy cream, scraping up any browned bits from the bottom of the pan. Simmer for 2 to 3 minutes to slightly thicken.
Stir in Parmesan and chopped parsley. Let the sauce simmer for another minute until smooth.
Return cabbage wedges to the skillet, spooning sauce over the top. Cover partially and cook for another 5 minutes, until cabbage is fork-tender.
Garnish with extra parsley and serve warm. Enjoy!
