Preheat your oven to 350°F (177°C) and prepare your baking sheets by lining them with parchment paper.

In a medium bowl, whisk together the all-purpose flour, cornstarch, baking powder, baking soda, salt, and matcha powder until well combined.

In a large bowl, use an electric mixer to beat the softened butter and granulated sugar together for 2-3 minutes.

Add the egg, sour cream (or Greek yogurt), and vanilla extract to the creamed butter and sugar. Mix until incorporated.

Gradually incorporate the dry ingredient mixture into the wet ingredients until a soft dough forms.

Using a 2-tablespoon scoop, portion the dough into balls and slightly flatten each ball before placing on baking sheets. Chill the cookies for about 20 minutes.

Arrange the cookies on your baking sheets and bake for 9-11 minutes until the edges are slightly golden.

Remove the cookies and allow them to cool on the baking sheets for a few minutes before transferring to a wire rack.

In a small bowl, heat milk until warm, steep the culinary lavender for about 10 minutes, then strain the lavender out and mix the infused milk into the butter and powdered sugar to make frosting.

Once the cookies are cool, frost each cookie generously with the lavender frosting.