Melt 2 tablespoons butter in a large skillet over medium heat. Add the flour and whisk to combine. Slowly add the milk while whisking constantly. Bring to a simmer and continue stirring until thickened, about 5 minutes.
Add the salt and pepper and stir to combine. Taste and adjust as needed. Add the cabbage and toss to coat. Cover with lid and cook for about 5 minutes.
Stir and cover again. Cook an additional 2-5 minutes to the desired doneness. Uncover and simmer to thicken as needed, just a minute or two longer. Stir in the remaining tablespoon of butter. Sprinkle with herbs, if desired. Serve warm.