Step 1: In the bowl of a stand mixer fitted with the paddle attachment, cream together the cold, cubed unsalted butter, granulated sugar, and light brown sugar on medium-high speed for 2-3 minutes, until light and fluffy.
Step 2: Reduce the mixer speed to low and add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract, scraping down the sides of the bowl as needed.
Step 3: In a separate medium bowl, whisk together the all-purpose flour, cake flour, cornstarch, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients in the mixer on low speed, mixing only until just combined and no dry streaks remain.
Step 4: Remove the bowl from the mixer and, using a spatula, gently fold in the dark chocolate chunks, milk chocolate chips, and chopped walnuts until evenly distributed. Do not add marshmallows yet.
Step 5: Divide the dough into 8 large, approximately 6-7 ounce (180-200g) balls. Place them on a parchment-lined baking sheet and chill in the refrigerator for at least 30 minutes, or up to 2 hours. While chilling, preheat your oven to 400°F (200°C).
Step 6: Arrange 4 chilled cookie dough balls on each of two parchment-lined baking sheets, leaving ample space between them. Bake for 10 minutes at 400°F (200°C).
Step 7: After 10 minutes, open the oven and gently press about 1 tablespoon of mini marshmallows onto the top of each cookie. Return the baking sheets to the oven and continue baking for another 4-6 minutes, or until the edges are golden brown and the centers are still soft and gooey, and the marshmallows are lightly toasted. Rotate baking sheets halfway through for even baking.
Step 8: Remove the cookies from the oven and let them cool on the baking sheets for 10-15 minutes before carefully transferring them to a wire rack to cool completely. This allows them to set properly and maintains their gooey centers.