For the pastry: In a mixing bowl whisk flour, salt and dry mustard together. Using a pasty cutter or two knives, cut the cold butter and shortening into the flour mixture until it looks like coarse crumbs. In a liquid measuring cup, combine the egg and vinegar and add enough ice water to make 2/3 cup (150 mL). Drizzle the egg mixture over the dry ingredients and stir with a fork until dough starts to come together. Divide the dough in half and form into discs. Wrap each disc in plastic wrap and refrigerate until chilled, at least 1 hour. (Pastry can be made and refrigerated two days ahead.)
For the filling: Heat olive oil in a large skillet and sauté onion with salt, pepper, mustard and spices. Add the carrot, garlic and herbs and sauté for 1 to 2 min over medium heat until spices start to become fragrant. Add the beef and sauté over medium heat, about 15 min. Add 1/4 cup (60 mL) of water to the mixture. Mix the cornstarch with the other 2 tbsp (30 mL) of water to make a slurry. Stir into the meat and simmer, 5 to 10 min until mixture is thickened. Take off the heat and let cool completely. (Meat mixture can be made 1 day ahead and refrigerated in an airtight container).
On a lightly floured clean surface roll out one pastry disc to 1/8” (3 mm) thick and approximately 12” (30 cm) in diameter to fit a 9” (23 cm) pie plate, allowing the extra pastry to fall over the sides. Spoon meat filling into pastry. Roll out second pastry disc, repeating size and thickness of the first. For the egg wash: Mix the egg and 1 tbsp (15 mL) of water together. Brush egg wash along the edge of pie shell. Trim pastry, leaving 1” (3 cm) dough over edge. Cover the pie with the second rolled out pastry. Press the edges of the pie to seal. Trim any excess dough and finish by crimping the edges of the pie.
Preheat oven to 400°F (200°C). Brush pie with remaining egg wash, cut steam vents in the top and bake in the lower third of the oven for 30 to 40 min or until top of tourtière is golden brown. Let rest for 10 to 15 min before serving.