Put the corned beef, carrots, and all but about 1 Tbsp of the onion into a large pot, cover with water, and bring to a boil over high heat. Reduce the heat to medium-low, and skim the foam from the surface of the water. Cover and simmer for about 2½ hours, or until the corned beef is tender. Remove from the liquid, wrap in foil, and set aside. Reserve about ¾ cup/175 ml of the cooking liquid.

Melt the butter in a small saucepan over medium heat. Mince the reserved onion and add to the butter. Cook for about 1 minute, then whisk in the flour and cook for about 1 minute more. Add the reserved cooking liquid, milk, parsley, mustard, nutmeg, and salt and pepper to taste, whisking the ingredients together until smooth. Cook 4 for 5 minutes more, whisking constantly, until the sauce thickens.

To serve, slice the corned beef and spoon the sauce over it.