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 until well combined.
03 - In a large bowl, 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 incorporated.
05 - Gradually add the dry ingredients to the wet mixture, mixing on low speed until just combined. Do not overmix.
06 - Scoop tablespoon-size portions of dough and roll into balls. Place on prepared baking sheets, spacing 2 inches apart. Slightly flatten each ball with your palm or the bottom of a glass.
07 - Bake for 10-12 minutes until edges are set but centers remain slightly soft. Cool on baking sheets for 3 minutes, then transfer to a 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 purple food coloring if desired.
09 - Once cookies are completely cool, spread or pipe lavender buttercream onto each cookie. Garnish with a pinch of culinary lavender buds.