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 just until combined and no dry streaks remain.
06 - Scoop tablespoon-size portions of dough and roll into balls. Arrange on prepared baking sheets, leaving 2 inches of space between each cookie.
07 - Gently press each dough ball with the palm of your hand or the bottom of a glass to slightly flatten.
08 - Bake for 10-12 minutes until edges are set but centers remain slightly soft. Cool on baking sheets for 3 minutes before transferring to a wire rack.
09 - While cookies cool, beat butter until creamy. Gradually add powdered sugar, then mix in milk, ground lavender, vanilla, and salt. Continue beating until light and fluffy. Add purple food coloring if desired.
10 - Once cookies are completely cooled, spread a generous layer of lavender buttercream over each. Sprinkle with additional lavender buds for garnish.