For the pastry, cut the cold butter into small cubes and rub it into the flour and a pinch of salt with your fingertips until it looks like coarse crumbs with some pea-sized pieces. Add 3 to 4 tbsp of ice water and press into a dough. Flatten into a disc, wrap and chill for at least 20 minutes.
Put the potatoes in a pot of cold salted water, bring to a boil over high heat and simmer over medium heat until soft, about 15 minutes. Drain and mash roughly.
Heat a large skillet over medium-high heat. Add the minced pork, turkey, onion and garlic and cook, breaking up the meat, until no pink remains and it reaches 71°C (160°F), about 10 minutes.
Add the broth, cinnamon, nutmeg, thyme, salt and pepper. Simmer over medium heat until most of the liquid is absorbed, about 15 minutes. Stir in the mashed potato and cool the filling for 15 minutes.
Preheat the oven to 200°C (400°F) with a rack in the lower third.
Spoon the filling into a 23 cm (9 inch) pie dish. Roll the pastry on a floured counter into a 28 cm (11 inch) round, about 3 mm thick, and lay it over the filling. Trim, fold the edge under and crimp with a fork.
Cut 4 small vents in the top for steam and brush with the beaten egg.
Bake for 30 to 35 minutes, until the pastry is deep golden and the filling bubbles through the vents. Cover the edges with foil if they brown too fast.
Rest for 10 minutes before cutting into 8 wedges. Serve with a green salad and a spoon of fruit ketchup if you like.
Tips
Serve with a sharp green salad and a spoon of fruit ketchup or chutney.