Prepare Pastry: In a large bowl, sift the gluten-free flour and xanthan gum. Add the grated cold butter and rub it into the flour until it resembles breadcrumbs.
Form Dough: Stir in the beaten egg and gradually add cold water, mixing until the dough comes together. Avoid overworking the dough. Wrap in cling film and chill for 30 minutes.
Roll and Cut: Preheat the oven to 180°C (350°F). Lightly flour a surface and roll out the chilled dough to about 3mm thickness. Use a 9cm cutter to cut 12 rounds for the bases and a 6.5cm cutter for the tops.
Assemble Pies: Gently press the pastry rounds into a greased muffin tin. Spoon 2 teaspoons of mincemeat into each case, ensuring not to overfill. Cover with the smaller pastry rounds or star-shaped cutouts.
Seal and Bake: Press the edges lightly to seal. Brush the tops with milk and sprinkle with sugar. Bake for 15 minutes, or until golden brown.
Cool and Serve: Allow to cool in the tin for 5 minutes, then transfer to a wire rack. Serve warm or at room temperature.