Preheat the oven to 300 F. Grease a 9-inch removable-bottom fluted tin and place this on a baking tray.
Beat the butter and brown sugar vigorously by hand or using beaters or a mixer fitted with the paddle attachment until pale and fluffy, about 3 minutes. It’s an important step to beat the butter and sugar well together when making shortbread – this ensures the shortbread will hold together and when you take a bite it will ‘snap’ and then melt away.
In a separate bowl, sift the flour, rice flour and salt. Add this to the butter and mix until blended. Using floured hands, press this into the prepared pan. Use a fork to dock the shortbread right through to the bottom and bake for 60 minutes, until just lightly browned. Immediately from the oven, slice the shortbread into 16 wedges, then cool completely in the tin.
This shortbread improves over a few days and can be frozen. Store in an airtight container for up to 10 days.