In a large skillet, brown the pork cubes, half at a time, in the oil. Season with salt and pepper. Set aside in a large saucepan.
In same skillet, brown the onion in remaining oil. Deglaze with the wine and add to the saucepan. Add the broth and bring to a boil. Cover and simmer gently for about 1 hour. Add the potatoes, duck, and stir to combine. Bring to a boil and simmer for 30 minutes, uncovered, or until the potatoes are tender. Adjust the seasoning. Let cool.
With the rack in the lowest position, preheat the oven to 190 °C (375 °F).
In a small bowl, combine the egg yolk and milk. Set aside.
In a food processor, pulse the flour and butter for a few seconds at a time until the butter is the size of peas. Add the eggs and water and pulse until the dough just begins to form. Add water, if needed. Remove the dough from the food processor and form into a disk with your hands.
On a floured work surface, roll out two-thirds of the dough to a 3-mm (1/8-inch) thick sheet. Line a 2.5 liter (10 cup) saucepan or baking dish, letting the dough hang on each side. Roll out the remaining dough into a disc a little larger than the dish.
Pour the meat mixture into the dish. Brush the edges of the dough with the egg wash. Top with the second piece of dough and seal it crimping the perimeter. Brush with the egg wash and make an incision in the centre of the dough. Bake for about 1 hour and 30 minutes. Let stand for about 20 minutes before serving.
If you prepare the braised pork the day before and it is cold, the cooking time will increase by about 30 minutes.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.