Brown the butter - Heat unsalted butter in a light colored saucepan over medium heat. Once the butter melts, it will become foamy. When the foam subsides, you will see clear bubbles, start whisking continuously at this point to keep the milk solids from burning. When the butter is caramel in color and smells nutty - about 8 to 9 minutes - take it off the heat and immediately pour it into the stand mixer bowl and allow to cool.
113 grams unsalted butter
Beat in sugar - Once the butter has cooled down, add both granulated sugar and brown sugar to it. Beat with the paddle attachment for at least 2 minutes until light in color.
50 grams granulated sugar, 100 grams brown sugar
Incorporate sourdough starter - Add the egg yolk, vanilla extract, sourdough starter and continue beating for at least another 2 minutes until fluffy and creamy.
1 large egg yolk, 3 grams pure vanilla extract, 60 grams sourdough starter discard
Add dry ingredients - Sift flour, matcha powder and baking soda directly into the wet ingredient mixture in the stand mixer bowl. Sprinkle the salt on top. Stir until incorporated. Stop the mixer and scrape down the sides and bottom of the bowl as necessary.
110 grams all-purpose flour, 9 grams matcha powder, 3 grams baking soda, 3 grams kosher salt
Add mix-ins - Add the white chocolate chips, stir to distribute evenly. Stop the mixer and use a spatula to scrape the side and bottom of the bowl to ensure good distribution of chocolate chips throughout the cookie dough.
86 grams white chocolate chip
Scoop and chill - Portion the cookie dough with a 3-tablespoon cookie scoop and place them on a lined baking sheet. Cover and refrigerate for at least 1 hour before baking.
Preheat the oven to 350°F.
Bake - Place 6 dough balls on a baking sheet, and bake 1 batch at a time for about 13 minutes, until the edges of the cookies start to turn lightly golden and the center is still slightly underbaked.
Cool - Remove the baking sheet from the oven, and allow the cookies to sit on the baking sheet to finish baking from the residual heat for 10-15 minutes before removing them to a wire rack to cool completely.