Preheat the oven to 350 degrees F (177 degrees C).
Prepare 2 baking sheets by covering them with parchment paper. Set aside.
Combine all purpose flour, matcha powder, baking soda, and salt in a bowl. Make sure to sift the matcha powder into the bowl to prevent clumping. Mix together and set aside.
Add the butter, sugar, and brown sugar to a large bowl. Whisk with a stand mixer or stand mixer with a paddle attachment for 2 minutes and the mixture is a light brown color.
Add the egg and whisk until incorporated.
Add the vanilla extract and whole milk. Whisk until incorporated.
Combine the wet ingredients with the dry ingredients from step 3. Mix with a spatula until just combined. Be careful not to over mix.
Add the white chocolate chips and mix until combined.
Use a 1 tbsp cookie scoop to scoop the cookie dough onto the prepared baking sheets. Bake for 10-12 minutes until the edges start to brown. If you want a really crispy cookie, I would recommend baking for 12 minutes.
Cool on the baking sheet for 10 minutes before transferring them to a cooling rack to cool completely.