Sift the ﬂour into a bowl and mix in the ground almonds, orange zest and sugar. Rub the butter into ﬂour mixture until the mixture resembles ﬁne breadcrumbs. Use a round-bladed knife and mix in the egg until the dough comes together. Gather the dough into a ball and knead briefly on a lightly ﬂoured work surface until smooth. Wrap in cling film; chill for 30 minutes.
Preheat oven to 200°C. Set out 20 tartlet tins. Roll out the dough very thinly; cut out 20 rounds 6 cm in diameter with a ﬂuted cookie cutter. Gather the trimmings and roll again very thinly; cut out 20 rounds 8 cm in diameter.
Place the larger rounds in the tins. Fill with fruit mince; top with 1 teaspoon brandy butter. Brush the edges of pastry with a little milk and place a smaller round on top of each pie, pressing the edges together to seal.
Brush the tops with the milk and make a hole in the lid of each pie to vent the steam. Bake in the centre of the oven for 25 minutes or until golden brown. Remove from oven, leaving the oven on, and cool the pies in their tins for 5 minutes, then lift out onto a wire rack to cool for 10 minutes.
For the icing, whisk the egg white until frothy, then beat in the sifted icing sugar. Spread a little icing over the top of the mince pies and arrange them on a baking tray. Bake at 200°C for 5–10 minutes or until the icing has browned a little and the pies are heated through. Leave them to cool for about 5 minutes before serving.