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 granulated 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 incorporated.
05 - Gradually add the dry ingredient mixture to the wet ingredients on low speed, mixing until just combined and a dough forms.
06 - Scoop tablespoon-size portions of dough and roll into balls. Arrange on prepared baking sheets with 2 inches of spacing between each cookie.
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 slightly soft. Allow cookies to cool on baking sheets for 3 minutes, then transfer to a wire rack to cool completely.
09 - Beat butter until creamy. Gradually incorporate powdered sugar, then mix in milk, ground lavender, vanilla, and salt. Continue beating until light and fluffy. Add food coloring if desired.
10 - Once cookies have cooled completely, spread lavender buttercream over each cookie using a small offset spatula. Garnish with a pinch of lavender buds.