In a medium-sized bowl, sift the flour, matcha powder, and salt together.
Using an electric mixer, cream the butter and powdered sugar together until light and fluffy.
Add the flour mixture, and mix together on low speed until combined. The mixture will be crumbly, but should hold together if you squeeze it in your hand.
Lightly dust your counter top with flour, and turn the matcha short bread out of the bowl.
Gather into a flat disc (if you're rolling and cutting) or form into a log (if you're slicing). Wrap with plastic wrap, and place in the fridge to chill for at least 30 minutes.
When you're ready to bake, preheat the oven to 325°F / 170°C. Line two large baking sheets with parchment paper.
Roll the chilled dough to 1/4-inch thick, and use cookie cutters to cut into shapes. Alternatively, slice the log into 1/4-inch slices.
Transfer the cookies to the prepared baking sheets, and place into the pre-heated oven.
Bake for 10-15 minutes (depending on the size of your cookies) until they are just beginning to turn brown around the edges.
Transfer to a wire wrack to cool completely, and serve with a nice cup of tea.