Prep: Preheat oven to 350°F and line a baking sheet with parchment paper. Set aside.
Mix dry ingredients: In a small bowl, stir together the flour, matcha powder, milk powder, baking powder, baking soda, and salt. Set aside.
Cream butter and sugar: In a large mixing bowl, use an electric hand mixer to beat softened butter until very creamy. Add sugar and cream together with the mixer until very creamy and fluffy, about 3-4 minutes.
Add eggs: Add in the eggs and vanilla extract and mix again until combined.
Add dry ingredients to wet ingredients: Add the flour mixture into the butter mixture and briefly mix with the hand mixer until almost combined with some flour patches left.
Fold in chocolate: Add the chopped chocolate and finish folding the dough together with a silicone spatula until just combined. Don't overmix.
Scoop cookie dough: Using a 4-tablespoon ice cream scooper, scoop out balls of cookie dough and place them on your baking sheet, leaving about 2" between each cookie for spreading.
Bake: Bake cookies for 12-14 minutes or until the edges are set but the middle is still very soft. In the last 2 minutes of baking, press a few extra white chocolate chunks on top of each cookie (optional).
Cool: Let the cookies cool on the baking sheet for 10 minutes before carefully transferring them to a wire rack to cool completely.