Prepare the Vegetables: Slice the cabbage into thin strips, dice the onion, and mince the garlic.
Sauté the Cabbage and Onion: In a large skillet or saucepan, melt 2 tablespoons of butter over medium heat. Toss in the cabbage and onion, sautéing for 6-8 minutes until they soften, stirring occasionally to avoid burning. Add the minced garlic and cook for an additional 1-2 minutes. Once done, remove the mixture from the pan and set it aside.
Make the Roux: In the same skillet, melt the remaining 2 tablespoons of butter over medium heat. Stir in the flour and cook for 1-2 minutes, continuously stirring, until the mixture thickens into a roux.
Create the Creamy Sauce: Gradually whisk in the milk and chicken broth, ensuring there are no lumps. Keep stirring and cooking for about 3-4 minutes until the sauce reaches a thicker consistency. Season with salt and pepper to your liking.
Combine and Heat Through: Return the sautéed cabbage, onion, and garlic to the skillet with the creamy sauce. Stir to coat the vegetables evenly in the sauce.
Serve and Enjoy: Transfer the creamed cabbage to a serving dish and enjoy as a side or a light main course.