Mix flour and salt in a bowl, then rub in butter and lard until reaching a breadcrumb consistency.
Incorporate 4 to 6 tablespoons of cold water to form a dough ball and refrigerate.
Sauté onion, carrot, and celery in oil for 5 to 10 minutes until soft.
Add the diced potatoes and cook for an additional 5 minutes.
Stir in corned beef, sauce, and beef stock, then simmer for 20 minutes until tender.
Season to taste and allow the filling to cool completely in a bowl.
Preheat the oven to 200°C and prepare a 23cm metal pie plate.
Roll out two-thirds of the pastry to 3mm thickness and line the pie plate.
Add parsley to the filling, spoon it into the plate, and cover with the remaining pastry lid.
Seal the edges, brush with egg, vent the top, and bake for 35 minutes until golden.