Step 1: Prepare the cabbage. Wash the cabbage thoroughly, remove any damaged outer leaves, and cut it into quarters. Remove the tough core from each quarter. Thinly slice the cabbage into ribbons, about 1/4 inch thick. Set aside.
Step 2: Sauté the aromatics. In a large skillet or Dutch oven over medium heat, melt the unsalted butter. Add the minced garlic and cook for about 1 minute until fragrant. Be careful not to let the garlic brown, as it can become bitter.
Step 3: Wilt the cabbage. Add the thinly sliced cabbage to the skillet with the garlic and butter. Sauté for 8-10 minutes, stirring occasionally, until the cabbage is tender-crisp and has significantly reduced in volume. Season the cabbage with 1/4 teaspoon of salt and 1/8 teaspoon of black pepper.
Step 4: Add the cream. Pour the heavy cream into the skillet with the cabbage. Bring the mixture to a gentle simmer, then reduce the heat to low. Let it simmer gently for 3-5 minutes to warm through and slightly thicken.
Step 5: Incorporate the cheese. Gradually add the freshly grated Parmesan cheese to the simmering cream, stirring continuously. Continue stirring until the cheese is completely melted and the sauce is smooth and creamy. If the sauce becomes too thick, you can add a splash of milk or vegetable broth to reach your desired consistency. Add the remaining salt and pepper, and a pinch of nutmeg if using. Taste and adjust seasonings as needed.
Step 6: Serve. Toss the cabbage ribbons thoroughly to ensure they are fully coated in the creamy Alfredo sauce. Serve the Cabbage Alfredo immediately, garnished with extra grated Parmesan cheese and fresh chopped parsley, if desired.