Sift the 2 flours (or flour and rice), sugar and salt into a mixing bowl. Rub in the butter with your fingertips. When the mixture starts to bind, gather it with one hand into a ball. Knead it on a lightly floured surface to a soft, smooth, pliable dough.
Put the dough in a 20 cm (8 inch) flan ring set on a greased baking sheet. Press it out with your knuckles to fit the ring. Mark the shortbread into 8 pieces using the back of a knife. Prick right through to the baking sheet with a fork in a neat pattern. Cover and chill for at least 1 hour before baking, to firm it up.
Bake in a preheated oven, 150°C (300°F), Gas Mark 2, for 45–60 minutes, or until the shortbread is a pale biscuit colour but still soft. Remove the shortbread from the oven and leave to cool and shrink before removing the ring, then dust lightly with caster sugar. When cold, cut into 8 pieces. It will keep, in an airtight container in a cool place, for a few days.