In a measuring cup, combine the water and vinegar. Set aside.
In a large bowl, combine the flour, baking powder, and salt. Add the shortening and cut with a pastry blender or two knives. Gradually add the water and vinegar mixture, stirring until the dough is smooth. Form the dough into eight discs. Cover in plastic wrap and refrigerate for 24 hours.
In a pan of salted water, cook the potatoes until tender. Drain. Using a masher, lightly crush the potatoes. Set aside.
In a large saucepan, soften the onion and garlic in the oil. Add the meat and the spices of your choice and sauté for about 5 minutes. Season with salt and pepper. Add the broth. Bring to a boil and simmer gently for about 30 minutes, stirring frequently. Add the potatoes and stir to combine. Adjust the seasoning. Let cool.
With the rack in the lowest position, preheat the oven to 190 °C (375 °F).
For each pie: on a generously floured work surface, roll out two discs of dough and line a 23-cm (9-inch) pie plate with one crust. Fill with a quarter of the meat mixture. Brush the edge with the beaten egg. Cover with the top crust. Tightly seal the pie by crimping the edge with your fingers. Brush with the beaten egg. Bake (two pies at a time or more, depending on the size of your oven) for about 1 hour or until the pastry is golden brown. If desired, freeze the pies before or after baking.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.