Preheat your oven to 350°F (177°C) and line your baking sheets with parchment paper.

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

In a large mixing bowl, cream the softened butter and granulated sugar together until light and fluffy.

Add the egg, sour cream, and vanilla extract to the mixture and beat until smooth and creamy.

Gradually stir the dry ingredients into the wet mixture until a thick cookie dough forms.

Scoop the dough into 2-tablespoon-sized balls, roll them gently, and flatten them slightly.

Refrigerate the shaped cookie dough for at least 20 minutes.

Bake the cookies for 9–11 minutes and watch closely until the edges are set.

Allow the cookies to cool on the baking sheets for a couple of minutes before transferring to a wire rack.

In a small saucepan, heat the whole milk over medium heat and steep the lavender buds for 4-5 minutes.

Strain the lavender-infused milk and beat it into the butter and powdered sugar until smooth.

Decorate the cooled cookies with the lavender frosting using a piping bag.

Store cookies in an airtight container in the fridge, layering with parchment if stacking.