In a large skillet, melt butter and olive oil over medium-high heat. Add cabbage wedges cut side down and sear for about 3-4 minutes until golden brown. Flip and sear the other side for another 3-4 minutes, then set aside.

Lower the heat to medium, add chopped onion, and sauté for about 5 minutes until golden and translucent. Scrape browned bits from the skillet.

Stir in minced garlic and Cajun seasoning, cooking for an additional minute until fragrant.

Pour in heavy cream, scraping the bottom of the skillet. Let it simmer for 2-3 minutes until slightly thickened.

Mix in Parmesan cheese and chopped parsley until cheese is melted. Return seared cabbage to the skillet, spooning sauce over each wedge.

Partially cover and cook for another 5 minutes over low heat until cabbage is fork-tender.