Warm up some light olive or vegetable oil in a large skillet over low-medium heat. Add the diced onion and sauce for 5 - 7 minutes, until soft and translucent.
Add the garlic, chilies, and allspice and sauté for a few more minutes.
Add the ground beef, increase the heat to medium, and cook for 5 minutes, until browned, using a flat wooden spatula to break it up as it cooks.
Add the grated potato, season with salt and pepper, cover and cook for another 10 or so minutes, stirring occasionally, until the potatoes and beef are cooked through. Taste and adjust salt and spices, if necessary.
Set the beef filling aside to cool completely and start preparing the pastry. You can make the filling in advance and refrigerate it until you’re ready to make a pies.
Preheat the oven to 375°F.
Dust your counter or surface with flour and roll out the dough until it’s 1-2mm thin, adding more flour to the surface as necessary.
Use the rim of a glass to cut out 3” circles, dipping the glass in flour in between cuts to prevent it from sticking to the dough.
Set the circles aside, collect the dough scraps, give them a few kneads to bring the dough together, and roll them out again. Repeat the cutting and collecting/rolling out scraps until all of the dough is used up.
Place a spoonful of dough on one of the circles, place another circle on top, and use your fingers to pinch it shut. Add as much filling as you can manage, without overflowing, and don’t worry if it’s not sticking too well. The next step will ensure that the pie gets sealed.
Place the pie down and use a flour-dusted fork to seal the perimeter.
Repeat with all of the pies and place them on a parchment-lined baking sheet. Brush them with the egg mixture, and bake for 30 - 40 minutes, until the pies are puffy, golden, and cooked through (you can check the inner temperature with an instant-read thermometer. It should be 160°F - 170°F).
Let them cool slightly before serving and refrigerate any leftover pies for up to 3 days. Reheat them in the oven, as necessary.
