Whisk together flour, curry powder, turmeric, salt, and sugar in a large bowl until evenly colored.
Cut cold butter and shortening into the flour with a pastry blender until the mixture resembles coarse crumbs with pea-sized pieces.
Add ice cold water one tablespoon at a time, mixing gently until dough just comes together. Avoid overworking.
Shape the dough into a flat disc, wrap in plastic, and refrigerate for at least 1 hour or up to overnight.
Heat olive oil in a cast iron skillet over medium-high heat. Brown ground beef for 6-8 minutes, breaking it up with a spoon. Drain excess fat.
Stir in onion, garlic, and Scotch bonnet pepper; cook for 3-4 minutes until softened. Add curry powder, allspice, and thyme; cook for 1 minute to bloom the spices.
Pour in beef broth, ketchup, and Worcestershire sauce. Reduce heat to low and simmer for 12-15 minutes until thick and glossy.
Stir in breadcrumbs and scallions; season with salt and pepper. Remove from heat and cool completely to room temperature.
Roll chilled dough to about 1/8 inch thickness on a floured surface. Cut 6-inch circles using a cookie cutter, gathering and rerolling scraps.
Place 2-3 tablespoons of cooled filling onto one half of each round. Brush edges with beaten egg wash, fold over, and press firmly to seal.
Crimp the sealed edges with a fork, then transfer to a parchment-lined baking sheet. Brush tops generously with egg wash.
Bake at 375°F for 30-35 minutes until deeply golden and flaky. Let cool for 5 minutes before serving.