Using a stand mixer, beat the butter for a couple of minutes until smooth and creamy. Add the salt and powdered sugar, then the egg, beating all the while and scraping the sides periodically until the batter is homogeneous. Add the matcha powder and flour and mix until just combined.
Cut the dough in half, shape into cylinders, and wrap in cellophane before placing in the fridge to cool for two hours. Alternatively, the dough can be placed in the freezer at this stage for up to 2 months. To use the frozen dough, defrost it for 10 min before proceeding with the rest of the instructions below.
Preheat the oven at 350°F (175°C) and line a baking sheet with parchment paper. Cut the cylinders in ¼ in (4 mm) slices, place on the baking sheet, and bake for 15 min until the edges are slightly golden.
Remove from the oven and let cool for 5 min before transferring the cookies to a cooling rack. Cookies can be stored up to 4 days in an airtight container.
For a winter holiday variation, try replacing the matcha with unsweetened dutch cocoa powder and adding a splash of orange extract. The matcha can also be replaced with powdered freeze-dried fruit, as long as the fruit has a sour or bitter flavor that will balance out the buttery sweetness of the cookie dough.