01 - Preheat oven to 350°F and line two baking sheets with parchment paper.
02 - In a medium bowl, whisk together flour, matcha powder, baking powder, and salt until well blended.
03 - In a large bowl, beat butter and sugar with an electric mixer on medium-high speed until light and fluffy, approximately 2-3 minutes.
04 - Add egg and vanilla extract to the butter mixture, mixing until fully incorporated and smooth.
05 - Gradually add the dry ingredient mixture to the wet ingredients on low speed, mixing until just combined. Do not overmix.
06 - Scoop tablespoon-size portions of dough and roll into balls. Arrange on prepared baking sheets, leaving 2 inches of space between each ball.
07 - Gently flatten each dough ball using your palm or the bottom of a glass to achieve even thickness.
08 - Bake for 10-12 minutes until edges are set but centers remain soft. Allow cookies to cool on baking sheets for 3 minutes before transferring to a wire rack to cool completely.
09 - Beat butter until creamy and smooth. Gradually incorporate powdered sugar, then add milk, ground lavender, vanilla, and salt. Continue beating until frosting becomes light and fluffy. Add purple food coloring if desired.
10 - Once cookies have cooled completely, spread or pipe lavender buttercream onto each cookie. Sprinkle with additional culinary lavender buds for garnish.