Brown the butter: In a light-colored saucepan over medium heat, melt the butter, swirling occasionally. Cook until it turns amber, brown specks form, and it smells nutty. Immediately remove from heat and pour into a large bowl to cool for 10-15 minutes.
Mix wet ingredients: To the cooled brown butter, add granulated and brown sugar. Beat for 2-3 minutes until smooth. Add vanilla, then eggs one at a time, mixing well after each addition.
Combine dry ingredients: In a separate bowl, whisk together flour, matcha powder, baking soda, and salt until no lumps remain and the matcha is evenly distributed.
Combine mixtures: With mixer on low, gradually add dry ingredients to wet ingredients. Mix just until combined and no flour streaks remain. Do not overmix.
Fold in white chocolate: Using a rubber spatula, gently fold in the white chocolate chips until evenly distributed throughout the dough.
Scoop and rest: Scoop 2-tablespoon sized dough balls onto a parchment-lined tray. Cover and let rest at room temperature for 15-20 minutes, or refrigerate for 30 minutes.
Bake: Preheat oven to 350°F (175°C). Place dough balls on parchment-lined baking sheets, 2 inches apart. Bake for 10-12 minutes, until edges are set but centers are still soft. Cool on baking sheet for 5 minutes, then transfer to a wire rack.
