With an electric mixer, beat butter, sugar, and vanilla extract together for a few minutes until light and fluffy.

In a separate bowl, combine flour, matcha powder, and salt, and gradually add this mixture to the butter mixture.

Gather and press the dough into a flattened disk and chill until firm, about 2 hours.

When ready to bake, preheat the oven to 325°F (165°C) and line 2 baking sheets with parchment paper.

Roll out dough to a ¼ inch (6mm) thickness on a floured surface and cut circles with a 2-inch (5cm) round cutter. Place cookies on the prepared baking sheet. Gather and reroll any scraps.

Sprinkle cookies with sugar, tapping gently so that the sugar sticks, and then bake for 18-22 minutes, until the cookies are dry and firm (they should not take on any color). Transfer to a wire rack to let cool completely.

Store in an airtight container at room temperature for up to 3 days.