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.
03 - Beat butter and sugar with an electric mixer until light and fluffy, about 2-3 minutes.
04 - Add egg and vanilla, mixing until fully incorporated.
05 - Gradually add dry ingredients to wet mixture, mixing on low speed until just combined.
06 - Scoop tablespoon-size portions of dough, roll into balls, and place 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. 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 - Frost completely cooled cookies with lavender buttercream. Garnish with a pinch of lavender buds.