In a food processor, pulse the flour, curry powder, turmeric, and salt together. Add the cold cubed butter and pulse until the mixture resembles coarse sand with pea-sized butter pieces remaining.

Drizzle in the ice water a tablespoon at a time, pulsing between additions, until the dough clumps when pressed. Shape into a disc, wrap tightly, and refrigerate for at least 30 minutes.

Heat oil in a large skillet over medium heat. Cook the onion for 4 to 5 minutes until translucent, then add garlic, thyme, and scotch bonnet and cook 1 minute more.

Add the ground chicken and cook, breaking it up, until no longer pink. Stir in the curry powder and toast for 30 seconds.

Pour in the chicken stock, bring to a simmer, and cook for 10 to 12 minutes, stirring occasionally, until the liquid reduces and the mixture holds together in a thick mound. Stir in the breadcrumbs and season to taste. Cool to room temperature.

Roll the chilled dough to ⅛-inch thickness and cut into 3.5-inch circles, re-rolling scraps once if needed.

Place 2 tablespoons of cooled filling on one half of each circle. Fold into a half-moon and press the edges together, then crimp firmly with a fork.

Arrange on a parchment-lined baking sheet, chill for 10 minutes, then brush with beaten egg.

Bake at 400°F for 25 to 28 minutes, until deep golden and firm. Rest for 5 minutes before serving.