In a large skillet or Dutch oven, heat 2 tablespoons of olive oil over medium-high heat. Allow the oil to shimmer, indicating it's hot enough for cooking.

Add the sliced andouille sausage to the hot skillet, spreading it in a single layer. Sear for about 5 minutes, stirring occasionally, until the sausage is browned and crispy on the edges.

Reduce the heat to medium and add 2 tablespoons of unsalted butter to the skillet, letting it melt completely. Toss in the diced yellow onion and sauté for about 4 minutes.

Stir in the minced garlic and cook for an additional minute, until fragrant.

Add the shredded green cabbage to the skillet, along with the remaining 4 tablespoons of butter, Cajun seasoning, and crushed red pepper flakes. Toss everything together and sauté for 7-9 minutes.

Pour in 1 cup of heavy whipping cream, stirring to combine. Bring to a gentle simmer over medium-low heat, allowing it to bubble softly for about 2-3 minutes.

Gradually add ½ cup of freshly grated Parmesan cheese into the sauce, stirring continuously until melted and the sauce thickens.

Return the seared sausage to the skillet, stirring everything to combine well, and adjust seasoning with salt and black pepper to taste.

Sprinkle freshly chopped parsley on top for a pop of color and freshness. Serve warm in shallow bowls.