Heat 2 tablespoons of butter and 1 tablespoon of olive oil in a large skillet over medium-high heat. Add quartered wedges of green cabbage and sear for 3-4 minutes on one side until golden brown, then flip and repeat. Remove cabbage from skillet.

In the same skillet, reduce heat to medium. Add chopped yellow onion and sauté for about 5 minutes until soft and golden.

Stir in minced garlic and Cajun seasoning into the onions. Cook for about 1 minute until garlic is fragrant.

Pour in heavy cream, scrapping up any browned bits from the skillet. Simmer gently for 2-3 minutes until thickened. Stir in Parmesan cheese and parsley until smooth.

Return the seared cabbage wedges to the skillet, spoon sauce over each piece, cover partially, and cook for about 5 minutes until cabbage is fork-tender.

Transfer the cabbage to a serving dish, adjust seasoning with salt and pepper, and garnish with parsley. Serve warm.