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

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

In a large mixing bowl, beat softened unsalted butter with granulated sugar using an electric mixer on medium speed for 2-3 minutes until light and fluffy.

Add the egg, sour cream, and vanilla extract to the creamed butter and sugar; mix on low speed until fully incorporated.

Gradually incorporate the dry ingredient mixture into the wet ingredients, gently folding until a thick dough forms.

Scoop 2-tablespoon portions of the dough and roll them into balls; place on prepared baking sheets and flatten slightly. Chill in the refrigerator for 20 minutes.

Bake for 9-11 minutes until the edges are set and centers look slightly underdone for a chewy texture.

Cool cookies on sheets for about 5 minutes, then transfer to a wire rack to cool completely.

While cookies cool, make lavender frosting by steeping culinary lavender buds in warm milk for 10 minutes, then strain and beat with softened butter and powdered sugar until smooth.

Frost each cooled cookie with lavender icing and store in an airtight container in the fridge.