We had some stunningly nice stem ginger shortbread over Christmas, and I've been looking around for a recipe to reproduce it. This is what I wound up with; largely borrowed from 'Leith's Cookery Bible', with some tweaks.
8 oz butter
4 oz caster sugar
8 oz plain flour
4 oz ground rice
2 oz crystallised stem ginger (finely chopped)
The theory is that you rub the butter and sugar together and then work in the flour/ground rice and ginger, until you have a 'smooth paste'. This is a whole lot easier if you have a food processor. Process the butter and sugar until they look like breadcrumbs and then add the flour and the ground rice, process a bit more and then add the ginger and give it a bit longer until it's all mixed. I was planning to mix the ginger in by hand but it actually turned out to be easier to do in the processor as it seemed to help to bind all the rest of the ingredients together a bit more. I was worried that the ginger would blend completely in with the rest of the ingredients but it doesn't seem to have done so.
Roll out to approx. 1/2" thickness and cut into rounds. Bake approx. 25 minutes, 150 degrees (about gas 3) until 'pale biscuit colour'.
Mine did not stay in their rounds, spreading rather, but they taste very nice!
The 'ginger' variation on the original recipe suggested adding about twice as much stem ginger and also some ground ginger as well. I have to say I think that'd be too much - though it may depend what ginger you're using. Two ounces was enough for them to be pleasantly tingly and interesting without losing the proper buttery shortbread flavour.