While the pastry is chilling, make the filling. Melt the butter over medium-high heat in a Dutch oven. Once the butter is bubbling, add the onion, celery, carrot, and garlic. Cook for about 5 minutes, until the vegetables have softened.
Stir in the potatoes and cook for another 5 minutes, then mix in the crumbled corned beef until well blended.
Pour in the beef stock, Worcestershire sauce, English mustard, and black pepper and stir until combined. Cover and bring to a boil.
Remove the lid and allow the mixture to simmer for about 15-20 minutes, until the potatoes and vegetables are cooked through, stirring occasionally.
Skim off any liquid that hasn't evaporated, then stir in the fresh chopped parsley.
Pour the filling into a 9 by 13-inch cake pan and chill in the freezer for 20 minutes, stirring halfway through.