There's a whole thread on Scottish shortbread that I started some time ago - here's my opening post in that thread.
I think that nearly every family in Scotland has its own recipe for shortbread - here's mine! It uses rice flour and gives a lovely light texture. I use an old wooden shortbread mould that it probably at least a hundred years old (getting a little cracked nowadays, but still makes a good round of shortbread!) The amounts I suggest fills that mould.
5 oz plain flour
3 tablespoons rice flour
2 oz caster sugar
4 oz butter
Sift flours together and add sugar. Work in butter with fingertips. Knead mixture lightly, but don't overwork or the butter will go oily.
Either use a shortbread mould or pack into a 7 inch sandwich cake tin. Make sure you 'prick' the mixture well with a fork to prevent it rising too much and making the results look 'bumpy'.
If you use a cake tin, mark the round into wedges before baking.
To make traditional 'petticoat tail' shortbread - lay the circle of shortbread on a baking tray, mark into wedges and then, using your fingers, make a scalloped edge to the dough.
Put in a heated oven Gas Mark 3, 160C or 325F for about 45 minutes until golden. When cool, dredge with a little caster sugar.
(Caster sugar is finer than granulated, but not as fine as icing sugar and I'm not sure what it's called in the USA or Canada!)
Keep in an airtight container and eat within a couple of days.