In a medium bowl, whisk together flour, matcha powder, baking powder and salt.
Beat butter on medium speed until smooth and creamy for about 20 seconds in the bowl of a stand mixer fitted with the paddle attachment, or use an electric hand mixer. Add sugar and beat on medium speed until pale and fluffy, about 1 ½ to 2 minutes. Scrape down the sides and bottom of the bowl, add egg and vanilla extract and beat on medium speed until well incorporated, 30-45 seconds. If the mixture still looks a tad bit curdled, it’s ok.
Add flour mixture in two batches and mix on low speed until it becomes moistened and forms a crumbly dough, about 15 seconds between additions. Remove the bowl from the mixer and finish mixing by hand using a rubber spatula until a soft dough forms.
Turn dough out onto a large piece of plastic wrap and use your hands to form it into a 9 to 10-inch long log (1.5 inches wide). Use the plastic wrap to help shape and roll it into a log. Place the log in the fridge and chill until firm, about 2 hours.
Preheat your oven to 350°F. Line two baking sheets with parchment paper and set aside.
Use a sharp knife to slice the log into squares about ¼ to ½-inch thickness and arrange slices on prepared baking sheets. These don’t spread much so you can fit quite a few on one tray.
Bake about 15 minutes until edges are lightly golden. Immediately transfer cookies to a wire rack to cool completely and enjoy!