For the pastry: Sift the flour, turmeric, and salt into a large bowl. Using your fingers, two knives, or a pastry blender, cut in the shortening and butter until mixture resembles coarse crumbs. Working quickly, add only enough water to form a firm dough. Do not overwork pastry. Form dough into a disc, wrap in plastic, and refrigerate for at least 1 1/2 hours or overnight.
In a large skillet, heat the oil until hot but not smoking. Add the onion and cook until softened, about 4 minutes. Add the garlic and ginger and cook for 1 minute. Add the ground beef, turmeric, cumin, allspice, cardamom, hot peppers, and thyme and cook until the beef is browned and spices are fragrant, about 10 minutes. Add the scallions, parsley, tomatoes, and stock and simmer for about 25 minutes, until the flavors have come together and almost all of the liquid has evaporated. Season, to taste, with salt and pepper, remove from the heat and stir in the rum. Set aside to cool before assembling the patties.
Preheat the oven to 400 degrees F.
On a lightly floured surface, roll out pastry and cut into circles about 6 to 7 inches in diameter. Spoon a scant 1/4 cup of the cooled filling onto the center of one side of each circle, and lightly brush the edges of the circle with a little of the beaten egg yolk mixture. Fold the other half of the pastry over so that the edges meet, and use a fork to crimp the edges together. Lightly brush the top of each patty with a little of the beaten egg yolk mixture. Place the patties on parchment-lined baking sheets and bake until golden brown, about 30 minutes. Serve immediately.
Yield: 8 to 10 patties