Step 1: Brown the Butter

1. Melt the Butter: In a medium saucepan, melt the butter over medium heat.
2. Brown the Butter: Continue cooking, swirling occasionally, as the butter foams and then begins to turn golden brown. After 5-7 minutes, you’ll see brown bits forming at the bottom of the pan, and the butter will smell nutty and aromatic. Be careful not to let it burn.
3. Cool the Butter: Remove the pan from heat and transfer the brown butter to a large mixing bowl. Let it cool for 10-15 minutes before proceeding.

Step 2: Prepare the Cookie Dough

1. Add Sugars to Butter: Once the brown butter has cooled slightly, add the granulated sugar and brown sugar to the bowl. Mix until the sugars are fully incorporated into the butter.
2. Add Eggs and Vanilla: Add the eggs and vanilla extract to the butter-sugar mixture, and beat until smooth and creamy.
3. Combine Dry Ingredients: In a separate bowl, whisk together the flour, matcha powder, baking soda, baking powder, and salt. This ensures that the matcha powder and leavening agents are evenly distributed.
4. Mix Wet and Dry Ingredients: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Avoid overmixing, as this can make the cookies tough.

Step 3: Chill the Dough

1. Chill the Dough: Cover the bowl with plastic wrap and chill the dough in the refrigerator for at least 30 minutes. Chilling allows the flavors to meld and prevents the cookies from spreading too much during baking.

Step 4: Shape and Bake the Cookies

1. Preheat Oven: Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat.
2. Portion the Dough: Use a cookie scoop or spoon to form balls of dough, about 1-2 tablespoons each. Place them on the prepared baking sheet, spacing them about 2 inches apart.
3. Optional Topping: If desired, press a white chocolate chunk or chip into the center of each dough ball and sprinkle with a pinch of flaky sea salt.
4. Bake: Bake in the preheated oven for 10-12 minutes, or until the edges are set but the centers are still slightly soft. The cookies will continue to cook on the baking sheet as they cool.
5. Cool on Wire Rack: Allow the cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.