In a medium bowl combine the turkey, onion, garlic, salt, pepper, cinnamon, and allspice. Mix thoroughly and refrigerate for one hour.
Preheat an oven to 350 degrees Fahrenheit and prepare a nine-inch pie pan by lightly oiling it with vegetable oil. Divide the pie pastry into two pieces and roll them out on a floured surface until they are just larger than the pie pan. Fit one piece of dough into the pan, then fill it with the turkey mixture. Brush the rim of the crust with beaten egg and place the remaining dough on top of the first. Make four small incisions in the top of the crust, and using a fork, crimp the edge of the pie to seal it.
Brush the surface of the pie with beaten egg, and bake for about one hour or until the crust is a rich golden-brown and the temperature of the thickest portion reaches 165 degrees. Allow the pie to cool for ten minutes before cutting.