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 dry ingredients to the wet mixture, mixing on low speed until just combined. Avoid overmixing.
06 - Scoop tablespoon-sized portions of dough and roll into balls. Place on prepared baking sheets, spacing 2 inches apart. Flatten slightly with palm or glass bottom.
07 - Bake for 10-12 minutes until edges are set but centers remain soft. Cool on baking sheets for 3 minutes, then transfer to wire rack to cool completely.
08 - Beat butter until creamy. Gradually add powdered sugar, then mix in milk, ground lavender, vanilla, and salt. Beat until light and fluffy. Add food coloring if desired.
09 - Once cookies are completely cool, spread lavender buttercream over each cookie. Garnish with additional lavender buds.