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-high 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. Do not overmix.
06 - Scoop tablespoon-sized portions of dough and roll into balls. Arrange on prepared baking sheets, leaving 2 inches of space 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 soft. Let cool on baking sheets for 3 minutes, then transfer to wire rack to cool completely.
09 - Beat butter until creamy. Gradually add powdered sugar, then mix in milk, ground lavender, vanilla, and salt. Continue beating until light and fluffy. Add purple food coloring if desired.
10 - Once cookies are completely cool, spread frosting over each cookie. Sprinkle with additional lavender buds for garnish.