In a food processor, place the flour and baking powder. Pulse for one second to combine. Add the butter and pulse for a few seconds at a time, until the mixture has a coarse and grainy texture. Add the egg, water and vinegar, pulsing a few seconds at a time, until a ball begins to form. Remove the dough from the processor. Form into a ball with your hands, dust with flour and cover with plastic wrap. Refrigerate for about 1 hour.
In a bowl, combine the egg and milk. Set aside.
In a skillet, brown the onions and garlic in the oil. Add the mushrooms and cook until their water has evaporated. Add the ground pork and cook, breaking it up with a spoon, until cooked through. Season with salt and pepper. Let cool. Add the remaining ingredients and stir to combine.
With the rack in the lowest position, preheat the oven to 350°F (180°C).
Roll out the dough. With a 5-inch (12.5 cm) round cookie cutter, cut 12 circles of dough. Line 12 muffin cups with the circles.
Spoon the filling into the dough. Brush the edges of dough with the egg wash.
With a 3 ½-inch (9 cm) round cookie cutter, cut 12 circles of dough. Place on the meat pies. Seal. Make an incision in the centre of each meat pie.
Bake for about 45 minutes or until the pastry is golden brown. Immediately unmould the meat pies and serve warm.
Unmould the meat pies right out of the oven. If they cool down, you may have a hard time unmoulding them.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.