Toast the Walnuts: Preheat oven to 350°F (175°C). Scatter chopped walnuts on a baking sheet and toast for 6-8 minutes until nutty and fragrant. Let cool completely before folding into dough.
Cream Cold Butter & Sugars: In a stand mixer fitted with the paddle attachment, beat the cold cubed butter, dark brown sugar, and granulated sugar on medium-high speed for 3-4 minutes until creamy but not overly warm or melted.
Add Eggs & Vanilla: Add cold eggs one at a time, followed by pure vanilla extract, beating on medium speed until just incorporated.
Whisk Dry Ingredients: In a separate bowl, whisk together all-purpose flour, cake flour, cornstarch, baking soda, and fine sea salt.
Fold into Thick Dough: Add dry ingredients to the butter mixture in two additions, mixing on lowest speed until barely combined with visible flour streaks (do not overmix). Gently fold in the toasted walnuts and chocolate chunks by hand until evenly distributed throughout the thick, heavy dough.
Shape Giant Mounds: Divide dough into 8 giant balls (about 5-6 oz each). Do NOT roll into smooth balls—roughly tear each dough portion in half and press the two halves back together with rough, jagged edges facing upwards for signature craggy bakery tops. Chill dough balls in the freezer for 15 minutes.
High-Heat Bake at 410°F: Preheat oven to 410°F (210°C). Line two large baking sheets with parchment paper. Place 4 chilled dough mounds spaced generously apart on each sheet. Bake for 10-12 minutes until the craggy tops are deeply golden and caramelized while the centers remain soft and puffed.
Cool & Sea Salt Shower: Immediately sprinkle hot cookies with flaky Maldon sea salt. Let rest undisturbed on the warm baking sheet for 15 minutes to allow the molten centers to set into gooey perfection before serving warm with cold milk!