01 - Preheat oven to 350°F and line two baking sheets with parchment paper.
02 - Whisk together flour, matcha powder, baking powder, and salt in a medium bowl until well blended.
03 - 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 ingredients to the wet mixture on low speed, mixing until just combined. Do not overmix.
06 - Scoop tablespoon-sized portions of dough and roll into balls. Arrange on prepared baking sheets with 2 inches of space between each cookie.
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 slightly soft. Cool on baking sheets for 3 minutes before transferring to a wire rack.
09 - Beat butter until creamy. Gradually incorporate powdered sugar, then mix in milk, ground lavender, vanilla, and salt. Whip until light and fluffy. Add purple food coloring if desired.
10 - Once cookies have cooled completely, spread lavender buttercream over each cookie and sprinkle with additional lavender buds for garnish.