Make the Pastry Dough: In a large mixing bowl, combine the flour, salt, and turmeric powder, making sure the vibrant yellow color is evenly incorporated. Using your fingertips, rub the cold butter into the flour mixture until crumbly texture resembling coarse breadcrumbs is achieved, ensuring small butter pieces remain for flakiness. Gradually add half a cup of ice-cold water, mixing with your hands to bring the dough together. Add more ice water, 2 to 3 tablespoons at a time, as needed until a soft but not sticky dough forms. To develop better flavor and texture, wrap the dough in plastic and refrigerate for 30 minutes. Make the Filling: In a spacious bowl, mix the minced beef with ground allspice and black pepper. Heat the vegetable oil in a skillet over medium heat until shimmering. Add the onions and sauté until translucent, about 3-4 minutes, then stir in the hot pepper, garlic, thyme, and a pinch of salt, cooking for an additional minute to release the aromas. Add the seasoned ground beef, breaking up any lumps, and cook until fully browned with no pink remaining. Stir in tomato ketchup and adjust salt to taste. Pour in two cups of water, bring to a boil, then reduce heat to a simmer. Let it cook uncovered until most of the liquid has evaporated and the filling thickens into a rich, saucy consistency. Fold in the chopped green onions, remove the skillet from heat, and allow the filling to cool completely before assembling. Assemble the Patties: Beat the egg with one tablespoon of water to prepare the egg wash and set aside. Option 1: Roll out one large piece of chilled dough on a floured surface into a broad circle. Using a bowl or cutter about five inches wide, cut out three circles. Place a generous three tablespoons of cooled filling on half of each circle. Moisten the edges with water using a moistened finger, fold over the pastry to cover the filling, and press firmly to seal. Option 2: Roll out each smaller dough piece to a 5-inch circle individually. Spoon the filling onto one side, moisten edges, fold over, and press to seal. In both methods, crimp the edges with the tines of a fork for a neat, decorative finish and trim any excess dough. Arrange patties on a parchment-lined baking sheet. Frying and Baking the Patties: Chill the assembled patties in the refrigerator to help them firm up while the oven preheats to 350°F (175°C). Before baking, brush each patty generously with the prepared egg wash to encourage a shiny, golden exterior. Bake in the preheated oven for 30 minutes or until the patties turn a deep golden brown and the pastry is crisp to the touch. Transfer the patties to wire racks to cool slightly before serving warm. Enjoy them fresh for the best flavor and texture. Tip: If you prefer an even flakier crust, handle the dough as little as possible and keep all ingredients cold. For an extra kick, include finely chopped Scotch bonnet peppers in the filling but handle with care!