1) Make the dough
In a large bowl, whisk together the flour, salt, curry powder, turmeric, and sugar. Add the cold diced butter and cut it in with a pastry cutter (or use your fingertips quickly) until you have pea-size pieces with some flatter shards.
Stir the vinegar into the ice water. Start with 6 tablespoons of the liquid, drizzling it in and mixing just until the dough looks shaggy. Add more water 1 teaspoon at a time only if needed, stopping as soon as it holds together when you squeeze a handful.
Turn onto the counter, press into a disk, wrap, and chill for at least 30 minutes.
2) Cook the filling
Heat the oil in a large skillet over medium-high heat. Add the ground beef and cook, breaking it up, until browned. If there is a lot of fat, spoon off a bit so the filling does not get greasy.
Add the onion and cook 3 to 4 minutes until softened. Add the garlic, thyme, curry powder, paprika, allspice, black pepper, salt, and Scotch bonnet if using. Cook 30 seconds, just until fragrant.
Stir in the tomato paste, then pour in the broth. Simmer 5 to 7 minutes, stirring, until the mixture thickens. You want it moist but not saucy. If it looks dry before the breadcrumbs go in, add a splash more broth.
Add breadcrumbs, scallions, and soy sauce if using. Cook 1 minute more.
Taste and adjust salt. Add lime juice if you want a brighter finish. Spread the filling on a plate to cool completely.
3) Roll and cut
Heat oven to 375°F. Line a sheet pan with parchment.
On a lightly floured counter, roll the chilled dough to about 1/8-inch thick. Cut circles about 6 inches wide (a bowl works). You should get about 10 circles; re-roll scraps once. If the dough starts shrinking or fighting you, let it rest 5 to 10 minutes, then roll again.
4) Fill, fold, and seal
Place about 1/4 cup cooled filling on one half of each circle, leaving a clean border. Lightly brush the edge with water, fold into a half-moon, and press to seal. Crimp with a fork.
Transfer to the sheet pan and chill 10 to 15 minutes if your kitchen is warm. This helps prevent leaks and boosts flake.
5) Egg wash and bake
Whisk egg and water. Brush a thin coat over the tops. Cut 1 to 2 small slits in each patty for steam.
Bake 22 to 27 minutes, until deep golden with browned edges and the crust feels firm to the touch. Cool 5 minutes before eating, unless you enjoy living dangerously.
