In a large mixing bowl, combine all-purpose flour, salt, and turmeric, stirring to blend well. Add cold butter and shortening, mixing until resembling coarse crumbs. Gradually pour in ice-cold water until dough just comes together. Shape into a disc, wrap in plastic, and refrigerate for 30 minutes.

Heat a skillet over medium heat, add ground beef, and brown it until no longer pink (about 5-7 minutes). Stir in onion, garlic, thyme, allspice, cayenne, black pepper, and salt. Cook for an additional 3-4 minutes. Mix in soy sauce, curry powder, and beef broth, then let it simmer for 10 minutes before adding breadcrumbs and removing from heat to cool.

Preheat oven to 375°F (190°C). Roll out chilled dough to 1/8 inch thick, using a 6-inch round cutter to cut circles. Place 2 tablespoons of cooled filling on one half, fold dough over, and seal edges with a fork.

Brush the tops with the beaten egg and arrange patties on the baking sheet. Bake for 20-25 minutes or until golden brown and flaky.