01 - In a large bowl, whisk together the all-purpose flour, salt, and ground turmeric. Add the cold cubed butter and cold cubed shortening. Cut the fats into the flour using a pastry blender or your fingertips until the mixture resembles coarse crumbs. Gradually stir in the ice water, one tablespoon at a time, just until the dough comes together. Divide the dough into two equal portions, shape each into a flat disk, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes.
02 - Heat the vegetable oil in a large skillet over medium heat. Add the finely chopped onion and minced garlic, and sauté until softened and fragrant, about 3 to 4 minutes. If using the Scotch bonnet pepper, stir it in now. Add the ground chicken and cook, breaking it apart with a spoon, until no longer pink throughout.
03 - Stir in the diced potato, Jamaican curry powder, ground allspice, dried thyme, black pepper, and salt. Cook for 2 minutes to bloom the spices. Pour in the chicken broth, cover the skillet, and reduce the heat to medium-low. Simmer for 8 to 10 minutes until the potatoes are tender and the liquid has thickened. Remove from heat, fold in the chopped scallions and fresh parsley or cilantro, and let the filling cool completely.
04 - Preheat the oven to 400°F. Line a large baking sheet with parchment paper and set aside.
05 - On a lightly floured surface, roll each chilled dough disk to approximately ⅛ inch thick. Using a 6-inch round cutter or bowl as a guide, cut out as many circles as possible. Gather and re-roll the scraps to yield a total of 8 rounds.
06 - Place 2 to 3 tablespoons of the cooled chicken filling onto one half of each dough round, leaving a small border around the edge. Fold the other half of the dough over the filling to form a half-moon shape. Press the edges together firmly and crimp with a fork to seal. Transfer each patty to the prepared baking sheet.
07 - Brush the top of each patty evenly with the beaten egg wash. Bake in the preheated oven for 25 to 30 minutes, until the pastry is golden brown and flaky. Allow the patties to cool on the baking sheet for 5 minutes before serving.