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 combined.
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.
05 - Gradually add dry ingredients to wet mixture, mixing on low speed just until flour disappears. Do not overmix.
06 - Scoop tablespoon portions of dough and roll into balls. Arrange on prepared baking sheets 2 inches apart. Flatten slightly with palm or glass bottom.
07 - Bake for 10-12 minutes until edges are set but centers remain soft. Let cool on sheets for 3 minutes before transferring to wire rack.
08 - Beat butter until creamy. Gradually incorporate powdered sugar, then mix in milk, ground lavender, vanilla, and salt. Whip until light and fluffy. Add food coloring if desired.
09 - Once cookies are completely cool, spread lavender buttercream over each cookie. Sprinkle with additional lavender buds for garnish.