Special equipment: a 5-inch round pastry cutter
For the pastry: Pulse the flour, curry powder and salt together in a food processor until well combined. Add the butter and pulse until the mixture resembles a coarse meal with some pea-size lumps. Add the vinegar and water, and pulse until the mixture forms a ball. Flatten the dough into a disc and wrap well in plastic. Refrigerate until firm, at least 1 hour.
For the filling: Heat the oil in a large skillet over medium-high heat. Add the beef and a pinch of salt and cook, breaking up any clumps, until brown, about 4 minutes. Add the onions and garlic and cook, stirring occasionally, until softened, about 6 minutes. Add the curry powder, thyme, allspice and cayenne; cook, stirring, for 1 minute. Add the Worcestershire sauce and 1 cup water and simmer until the flavors have blended and the liquid has evaporated, about 10 minutes. Add salt to taste.
For the patties: Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
On a lightly floured work surface, roll out the dough to an approximately 14-inch circle, a little more than 1/8-inch thick. Cut out eight 5-inch rounds. Spoon about 1/4 cup of the filling into the center of each round, then fold into a half-moon shape, carefully stretching the dough slightly if necessary to enclose the filling. If needed, use a little water to seal the edges. Press the tines of a fork along the seams to help seal.
Arrange the patties on the prepared baking sheet. Whisk the egg with 1 tablespoon water and lightly brush the patties with the egg wash.
Bake until golden all over and cooked through, 30 to 35 minutes. Let cool for 5 minutes before serving. Serve with hot sauce.