Place the butter and sugar in a bowl and cream together until light, plae and fluffy. Alternatively, process them in a food processor, then scrape the mixture into a bowl.
Sift together the flour, ground rice and salt and stir into the butter and sugar with a wooden spoon, until the mixture resembles fine breadcrumbs.
Working quickly, gather the dough together with your hand, then put it on a clean work surface. Knead lightly together until it forms a ball, but take care not to over knead or the shortbread will be tough and greasy. Lightly roll into a sausage shape about 3 inch thick. Wrap the roll of dough in clear film and chill until firm.
Preheat oven to 375 derees. LIne 2 baking sheets with baking parchment.
Pour the sugar on to a sheet of parchment. Unwrap the dough an roll it in the sugar until evenly coated. Using a large, sharpknife, slice the roll into discs anbout 1/2 inch thick.
Place the dics on to the baking sheets, spacing them well apart. Bake for 20 - 25 minutes until very pale gold in color.
Remove from the oven and sprinkle with sugar. Leav to cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.