- In a large saucepan over medium-high heat, brown the onion and garlic in 3 tbsp (45 ml) of the oil. Add the meat. Continue cooking until the meat is cooked (but not browned). Add the tomato paste and mix thoroughly.
- Deglaze with the wine and broth. Bring to a boil. Cover and simmer for 1 hour. Add the carrot and celery and continue cooking for about 30 minutes or until the meat is fork tender.
- In a small bowl, dissolve the cornstarch in the water. Add the cornstarch mixture to the filling and bring to a boil while stirring. Season with salt and pepper.
- In a skillet over medium-high heat, brown the mushrooms in the remaining oil (2 tbsp/30 ml). Add the mushrooms and peas to the beef mixture. Set aside.
- In a food processor, combine the flour and salt. Add the butter and pulse a few seconds at a time until pea-sized pieces form. Add the water and vinegar. Pulse again until the dough just begins to form. Add water if needed. Remove the dough from the food processor and shape into two discs. Cover with plastic wrap and refrigerate for 15 minutes.
- With the rack in the middle position, preheat the oven to 400°F (200°C).
- On a floured work surface, roll out the two discs of dough and line a 9-inch (23 cm) pie plate with one sheet. Spoon in the beef mixture. Make incisions in the centre of the second sheet of dough to allow steam to escape during cooking. Cover the filling with this sheet and crimp the edges. Brush with milk.
- Bake for about 40 minutes or until the crust is golden brown. Let rest for 15 minutes before serving.
The meat can be cooked in advance. You can also freeze the meat pie once it’s been cooked.