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.
03 - In a large bowl, beat butter and sugar with an electric mixer until light and fluffy (2-3 minutes).
04 - Add egg and vanilla, mixing until combined.
05 - Gradually add the dry ingredients to the wet mixture, mixing on low until just incorporated.
06 - Scoop tablespoon-size portions of dough and roll into balls. Place on prepared baking sheets, spacing 2 inches apart.
07 - Slightly flatten each ball with your palm or the bottom of a glass.
08 - Bake for 10-12 minutes, until edges are set but cookies are still soft. Cool on baking sheets for 3 minutes, then transfer to a wire rack to cool completely.
09 - Beat butter until creamy, then gradually add powdered sugar. Mix in milk, ground lavender, vanilla, and salt. Beat until light and fluffy. Add a drop of purple food coloring if desired.
10 - Once cookies are completely cool, frost each with lavender buttercream. Garnish with a pinch of lavender buds.