01 - In a large bowl, whisk together the flour, salt, and ground turmeric. Add the cold cubed butter and shortening, then cut them in using a pastry blender or your fingertips until the mixture resembles coarse crumbs. Gradually drizzle in the ice water, stirring gently until the dough just comes together. Divide the dough in half, shape each portion into a flat disk, wrap tightly in plastic, and refrigerate for at least 30 minutes.
02 - Heat the vegetable oil in a large skillet over medium heat. Sauté the chopped onion and minced garlic until softened and fragrant, about 3 minutes. Add the minced Scotch bonnet pepper if desired, then crumble in the ground chicken. Cook, breaking the meat 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, then pour in the chicken broth. Cover the skillet and simmer for 8 to 10 minutes, until the potatoes are tender and the filling has thickened. Fold in the chopped scallions and parsley, remove from heat, and allow the filling to cool completely.
04 - Preheat the oven to 400°F. Line a baking sheet with parchment paper and set aside.
05 - On a lightly floured surface, roll each chilled dough disk to approximately ⅛ inch thick. Cut out 6-inch circles using a bowl or round cutter as a template. Re-roll any scraps to yield a total of 8 rounds.
06 - Spoon 2 to 3 tablespoons of the cooled chicken filling onto one half of each dough round. Fold the other half over the filling to form a half-moon shape. Press the edges firmly with a fork to crimp and seal. Transfer each patty to the prepared baking sheet.
07 - Brush the top of each patty evenly with the beaten egg wash. Bake for 25 to 30 minutes until the pastry is deeply golden brown and flaky. Allow the patties to cool for a few minutes on the baking sheet before serving.