Heat the olive oil in a large, deep skillet over medium-high heat until shimmering.
Add the sliced pork-free Andouille sausage to the hot oil and cook for 3-4 minutes, turning occasionally, until browned on both sides.
Once browned, transfer the sausage to a plate lined with paper towels and set aside.
Add 4 tablespoons of butter to the same skillet, swirl to melt. Cook the onion for 2-3 minutes until softened.
Stir in the chopped cabbage and remaining 2 tablespoons of butter. Cook for 6-8 minutes, stirring occasionally, until tender.
Return the cooked sausage to the skillet with the cabbage mixture. Add the heavy cream and simmer on low heat for 5 minutes.
Stir in Parmesan cheese and Cajun seasoning, then adjust seasoning and add a splash of heavy cream if needed for a saucier texture.
Season with salt and pepper to taste.
Transfer to serving plates, garnish with fresh parsley, and serve warm.