Prep and Chill Flour: Sift together the bread flour, cake flour, matcha powder, fine salt, baking powder, and baking soda into a large bowl. Place the dry ingredients, along with your diced cold butter, into the refrigerator to chill for 15 minutes before starting.
Pulse the Base: Transfer the chilled flour mixture, cold diced butter, granulated sugar, and light brown sugar into a food processor. Pulse for 15 to 20 seconds until the butter is completely broken down and the mixture looks like fine, wet sand. Pour it back into a large mixing bowl.
Fold in Mix-ins: Add the chopped white chocolate chunks and toasted macadamia nuts to the bowl. Toss everything together with a spatula until the chunks are evenly distributed through the sandy flour base.
Add the Eggs: Lightly beat the cold eggs, then pour them into the bowl. Mix with a spatula until a rough dough starts to form. Use your hands to gently press and scrub the dough together a few times against the side of the bowl until it just holds. Do not overknead.
Portion and Freeze: Divide the dough into large, heavy portions weighing about 4 ounces (110g) each. Shape them roughly into tall balls—leave the surface textured and bumpy for a rustic look. Place them on a parchment-lined tray and freeze for at least 1 hour.
Preheat and Arrange: Preheat your oven to 375°F (190°C) for a classic chew, or 400°F (205°C) if you prefer them ultra-gooey. Line a large sheet pan with a silicone baking mat or parchment paper and space the frozen dough balls 3 inches apart.
Bake to Perfection: Bake at 375°F (190°C) for 20 to 25 minutes until the bottoms are lightly golden-brown. (If baking at 400°F for a molten center, bake for 15 to 20 minutes instead).
Cool Slightly: Let the cookies rest on the hot pan for 5 minutes to set, then carefully move them to a wire cooling rack to finish cooling.