Prepare two large baking sheets with parchment paper or silicone mats. Arrange your oven rack to the center position and preheat your oven to 325°F.
In a medium bowl, whisk the flour, cornstarch, salt, and matcha powder. Set aside.
In a large bowl or stand mixer, use an electric mixer or the paddle attachment to beat the softened butter until smooth and creamy with no lumps. Add the granulated and brown sugar and beat until they are well combined with the butter and the mixture is light and fluffy. Mix in the egg and vanilla extract on low speed until just combined. Wipe down the sides of the bowl with a rubber spatula.
Mix in the dry ingredients on low speed until the dough comes together. It will be pretty thick. Stir in the white chocolate chips (if using) on low speed until evenly distributed throughout the dough.
Scoop about 1 and ½ tablespoons of dough (30 grams) and roll it into a ball with the palm of your hand. Roll the balls in sugar, if desired (adds a crisp, sparkly exterior). Arrange the dough on the prepared baking sheets, about 2-3 inches apart.
Use the bottom of a clean glass to gently flatten the dough balls into ½"-thick round discs. Dip the bottom of the glass in a little sugar if it starts to stick to the dough.
Bake the cookies in the preheated oven, one baking sheet at a time, for 12 minutes each. Allow the cookies to cool on the pan for about 5 minutes before transferring to a plate or a wire cooling rack.
Store cookies in an airtight container and keep at room temperature for 4-5 days.