Cook butter, apples, brown sugar, lemon juice and cinnamon in a covered saucepan over medium heat for 5–6 minutes, until fork-tender. Stir in the cornstarch slurry and cook, stirring, about 1 minute until the juices thicken. Spread in a shallow dish and cool completely.

Combine the pastry flour, sugar, xanthan and salt. Work in the cold butter, leaving large pieces about the size of walnut halves. Add cold water gradually while tossing, just until all the flour is damp and the dough can be pressed together. Wrap and refrigerate 20–30 minutes.

Roll on a floured surface into a long rectangle about 1/4 inch thick. Fold in thirds like a letter, rotate a quarter turn and roll again. Repeat until you have made three letter folds in total. Wrap and chill another 20–30 minutes.

Roll the chilled pastry to 1/8 inch / 2–3 mm thick. Cut 5–5 1/4-inch circles, stacking and rerolling scraps to make 9–10. Place 1 1/2–2 tbsp cold filling on half of each circle, leaving a 1/2-inch border. Brush the border with egg, fold over, seal and crimp with a fork.

Freeze the covered assembled pies at least 15 minutes, until firm. Heat a conventional oven to 400°F / 200°C. Move to a fresh lined tray, add two vents to each pie, brush with egg and sprinkle with sugar.

Bake 25–30 minutes, until deeply golden. Rest 5 minutes on the tray, then cool on a rack. The filling is hot immediately after baking; serve warm or at room temperature.