For the Dough: In the bowl of a food processor, pulse together flour, salt, curry powder, turmeric, and butter until butter is broken into pea-size pieces, about 10 pulses.

In a small bowl, whisk together water, vinegar, and egg. Add the mixture to food processor and pulse until dough is combined (will still look loose but should hold together when you ball up a bit in your hand). Turn dough out onto a lightly floured surface and shape into a 2-inch-thick disk. Wrap dough in plastic wrap and refrigerate for at least 1 hour or up to overnight.

For the Filling: In a large sauté pan over medium-high heat, brown ground beef, breaking meat into little bits and stirring occasionally. When beef is nearly cooked through, about 6 minutes, reduce heat to medium and add onion, Scotch bonnet pepper, and garlic. Cook, stirring often, until vegetables have softened, 4 to 5 minutes.

Add broth, Pickapeppa sauce, Worcestershire sauce, onion powder, cayenne, curry, allspice, salt, bay leaves, and thyme to beef mixture in sauté pan, stirring to combine. Bring to a boil over high heat; reduce heat to medium low, and simmer, stirring occasionally, until most of the liquid has evaporated, about 12 minutes. Remove from heat. Discard bay leaves and thyme sprigs. Season with additional salt to taste, if needed. Add breadcrumbs and stir thoroughly.

Adjust oven rack to lower-middle position and preheat oven to 375°F (190°C).

Flour your work surface and rolling pin. Roll out dough to an ⅛-inch thickness. Cut dough into 6-inch circles and place 2 heaping tablespoons of meat filling onto half of each round of dough. Brush edges of dough with egg wash. Fold dough over filling to make a half-moon shape. Press edge with tines of a fork to seal. Brush tops lightly with remaining egg wash.

Set patties on a parchment paper-lined rimmed baking sheet and bake until dough is golden brown and cooked through, about 25 minutes. Let stand 5 minutes before serving.