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 evenly blended.
03 - Beat butter and sugar with an electric mixer on medium speed until light and fluffy, approximately 2-3 minutes.
04 - Add egg and vanilla extract to the butter mixture, mixing until fully combined.
05 - Gradually add dry ingredients to the wet mixture on low speed, mixing until just incorporated. Do not overmix.
06 - Scoop tablespoon-size portions of dough and roll into balls. Arrange on prepared baking sheets with 2 inches of spacing between each ball.
07 - Gently press each dough ball with your palm or the bottom of a glass to slightly flatten.
08 - Bake for 10-12 minutes until edges are set but centers remain soft. Cool on baking sheets for 3 minutes, then transfer to a wire rack to cool completely.
09 - Beat butter until creamy, then gradually incorporate powdered sugar. Add milk, ground lavender, vanilla, and salt. Whip until light and fluffy. Add purple food coloring if desired.
10 - Once cookies have cooled completely, spread a layer of lavender buttercream over each cookie. Sprinkle with additional lavender buds for garnish.