Mix together the currants, candied peel, mixed spice and muscovado sugar in a bowl.
Roll out the pastry thinly on a lightly floured surface and cut out 10 rounds using a 12–13 cm (5–5½ inch) plain biscuit cutter or by cutting around a small bowl, re-rolling the trimmings to make more.
Brush the edges of the rounds with beaten egg and spoon the currant mixture into the centres. Bring the edges of the pastry up over the filling and pinch firmly together. Turn the cakes over and flatten under the palms of your hands. Place slightly apart on a large greased baking sheet and make several deep cuts over the top of each, through to the filling. Brush with beaten egg.
Bake in a preheated oven, 220°C (425°F), Gas Mark 7, for about 15 minutes until deep golden and puffed. Sprinkle with caster sugar, then transfer to a wire rack to cool.