Preheat the oven to 190°C (375°F/Gas 5). Lightly grease two baking trays.
Cream the butter and sugar in a bowl using electric beaters until pale and fluffy. Sift in the flour, rice flour and a pinch of salt and, using a wooden spoon, stir into the creamed mixture until it resembles fine breadcrumbs. Transfer to a lightly floured work surface and knead gently to form a soft dough. Cover with plastic wrap and refrigerate for 30 minutes.
Divide the dough in half and roll out one half on a lightly floured work surface to form a 20cm (8inch) round. Carefully transfer to a prepared tray. Using a sharp knife, score the surface of the dough into eight equal wedges, prick the surface lightly with a fork and, using your fingers, press the edges to form a fluted effect. Repeat this process using the remaining dough to make a second round. Lightly dust the shortbreads with the extra sugar.
Bake for 18–20 minutes, or until the shortbreads are light golden. Remove from the oven and while still hot, follow the score marks and cut into wedges. Cool on the trays for 5 minutes, then transfer to a wire rack to cool completely. The shortbread will keep, stored in an airtight container, for up to 1 week.