Preheat the oven to 400 degrees. Lightly grease a baking sheet and set aside.
In a medium sauté pan, heat up oil over medium heat and brown beef, onion, and pumpkin. Add grated garlic, salt, fresh cracked pepper, and thyme, and cook until beef is fully done, stirring often. Set aside to cool until the mixture can be handled.
Cut each sheet of pastry into 4 equal squares. Divide beef mixture among the pastry squares, placing it right in the center.
Lightly rub the edges of the squares with water and pinch them together to form rectangle hand pies.
Whisk egg white with a splash of water, and brush all the pies.
Bake hand pies for about 15 minutes, until the dough is golden brown.