Place the corned beef with spice packet into a large pot. Add the carrots, onion less 1 tablespoon into a large pot. Cover with water and bring to a boil over high heat. Reduce heat to medium-low and skim the foam from the surface of the water.
Cover and simmer for about 2 ½ hours, or until the corned beef is tender. Add the cabbage and cook for another 5 minutes and let it rest in the pan with the juices until tender.
Remove from the liquid, wrap in foil and set aside. Reserve about ¾ cup of the cooking liquid.
Melt the butter in a small saucepan over medium heat. Mince the reserved onions and add to the butter.
Cook for about 1 minute then whisk in the flour and cook for another 1 minute more.
Add the reserved liquid, milk parsley, mustard, nutmeg and salt and pepper to taste whisking the ingredients together until smooth
Cook for another 5 minutes more, whisking constantly, until the sauce thickens.
Serve over slices of corned beef and spoon the sauce over it.