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.
Giangi's Kitchen provides nutritional information, but these figures should be considered estimates, as a registered dietician does not calculate them.