In a medium bowl, whisk together the gluten free all-purpose flour, matcha green tea powder, baking soda, and salt. Set aside.
In a large bowl, whisk the melted unsalted butter, brown sugar, and granulated sugar until well combined and smooth.
Whisk in the egg, egg yolk, and vanilla extract into the butter mixture until glossy.
Fold the dry matcha mixture into the wet ingredients using a rubber spatula until just combined, being careful not to overmix.
Gently stir in the white chocolate chips. Cover the bowl and chill the dough in the refrigerator for at least 30 minutes.
Preheat the oven to 350F. Scoop 2-tablespoon sized balls of dough onto a parchment-lined baking sheet, spacing them 2 inches apart.
Bake for 10-12 minutes until the edges are set but the centers are still soft. Cool on the pan for 5 minutes before transferring to a wire rack.