Rinse the corned silverside under cold running water to remove any excess surface brine.
Place the silverside into a large stockpot. Add the onion, carrot, celery, bay leaves, peppercorns, cloves, brown sugar and malt vinegar. Pour in enough cold water to completely cover the beef.
Bring the water to a gentle simmer over medium-high heat. As it begins to simmer, skim away any foam that rises to the surface.
Reduce the heat to low, cover with a lid and cook at a very gentle simmer for 2½–3 hours, or until the corned beef is fork tender. Avoid boiling, as this can make the meat tough.
Carefully lift the corned beef from the cooking liquid and transfer it to a chopping board. Loosely cover with foil and rest for 10 minutes before slicing across the grain.
While the beef is resting, melt the butter in a medium saucepan over medium heat. Stir in the flour and cook for 1–2 minutes, stirring constantly, to form a smooth roux.
Gradually whisk in the milk a little at a time, whisking well after each addition until completely smooth, then whisk in the 125 ml reserved cooking liquid. Continue cooking, stirring regularly, until the sauce thickens enough to coat the back of a spoon.
Whisk in the Dijon mustard, then stir through the chopped parsley. Season with salt and white pepper to taste.
Slice the corned beef across the grain and serve with the warm parsley sauce, buttered potatoes and your favourite vegetables.