Start by preheating your oven to 175°C (350°F). Line a baking tray with parchment paper so your cookies bake evenly and release easily.
Melt butter in a saucepan over medium heat. Stir continuously as it foams and bubbles. Once golden brown bits form and a nutty aroma develops, remove from heat and allow it to cool slightly.
In a bowl, whisk together flour, matcha powder, baking soda, and salt. This helps distribute everything evenly and prevents lumps.
In another bowl, combine cooled brown butter with white and brown sugar. Whisk until smooth and glossy, then mix in the egg until fully incorporated.
Slowly fold dry ingredients into the wet mixture. Mix gently until just combined, then fold in chopped white chocolate chunks.
Scoop dough portions onto the lined tray, leaving enough space between cookies. Press a few extra chocolate pieces on top for a bakery-style look.
Bake for 10–13 minutes until edges are lightly golden and centers remain soft. Cool on the tray for 5 minutes before transferring to a wire rack.