In a large mixing bowl, whisk together the all-purpose flour, salt, sugar, and ground turmeric until well combined. Cut in the cold unsalted butter until the mixture resembles coarse crumbs. In a separate bowl, combine the ice water and white vinegar, then gradually add to the flour mixture, stirring until combined. Divide the dough into two discs, wrap in plastic, and chill in the refrigerator for at least 30 minutes.

Heat a tablespoon of vegetable oil in a skillet over medium heat. Sauté the chopped onion, scallions, minced garlic, and Scotch bonnet pepper for about 3 minutes until softened. Add the ground beef, breaking it apart, and cook until browned. Gradually mix in ground allspice, dried thyme, paprika, cayenne pepper, salt, and black pepper. Stir in ketchup and beef broth, simmer for 10 minutes until thickened. Set aside to cool.

Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper. On a floured surface, roll out the chilled dough to 1/8 inch thick, cut into 6-inch circles. Place 2 tablespoons of beef filling onto one half of each circle, brush edges with water, fold, and crimp to seal. Arrange patties on baking sheet.

Carefully bake the patties for 25-30 minutes, or until golden brown. Let cool for a few minutes before serving.