I found this recipe on the Culinaryteas.com web site. I'm always on the look out for interesting recipes using green tea, so here it is! Note: the preparation time does not include the time to chill the dough.
Cream butter in the bowl of an electric standing mixer using the paddle attachment; add confectioner's sugar and salt.
Sift together the tea and flour and add to the butter mixture; mix until just incorporated.
Roll the dough out to about 1/3-inch thick between 2 pieces of plastic wrap; transfer to a baking sheet and chill until firm, at least 30 minutes.
Heat oven to 300 degrees.
Remove top piece of plastic and cut into desired shapes; re-roll excess dough as necessary; transfer to a parchment-lined baking sheet.
Bake for 16 minutes; rotate pan and bake for another 16 minutes, or until they feel firm when scratched with a fingernail; take care not to let the edges brown; matcha shortbread cookies should maintain their green color.
Cool, and serve with green-tea or ginger ice cream.