In a bowl, sift matcha powder and whisk with warm water until smooth.
Add milk and honey to the matcha mixture and stir well.
Fill a glass with ice, pour in the matcha blend, and shake to chill.
Preheat the oven to 350°F (175°C).
Mix flour, baking powder, baking soda, and salt in a bowl.
In another bowl, cream butter and sugar until light and fluffy.
Add the egg, lemon zest, lemon juice, and vanilla extract to the butter mixture.
Gradually mix in the dry ingredients.
Scoop dough onto a baking sheet and bake for 10-12 minutes.
Cool cookies on a rack and serve with iced matcha.