Preheat the oven to 350°F and line a large baking sheet with parchment paper and set it aside.
In a bowl, combine 2 cups plus 2 tablespoons of all purpose flour, 1 tablespoon of corn starch, 1 teaspoon of teaspoon of kosher salt, and ¾ teaspoon baking soda. Set aside.
In a separate bowl, cream together 12 tablespoons of softened unsalted butter, ¾ cup of brown sugar, and ½ cup of granulated sugar, until smooth and creamy, about 3-4 minutes.
Mix in 1 tablespoon of vanilla extract and 1 teaspoon of cake batter extract until totally combined.
Mix in the egg and the egg yolk until totally combined and smooth. Make sure to scrape the sides of the bowl to ensure everything is incorporated.
Sift in the dry ingredients. Mix gently to incorporate using a rubber spatula. When the dough is almost all of the way mixed (there may still be streaks of flour), fold in the Lucky Charms marshmallows. Make sure to scrape the sides of the bowl to ensure everything is incorporated.
Use a large cookie scoop (#20) to get nice big balls of cookie dough.
Place the cookies on a baking sheet a few inches apart. This will make 12-14 cookies. We'd recommend chilling the cookies for 30 minutes - 2 hours, or even overnight if you have the time, though it is not entirely necessary and the cookies can be baked right away.
When it's time to bake, place 5-6 cookies on a baking sheet with plenty of room in between them so they can spread. Bake at 350°F until the edges are set, about 13-15 minutes. Let the cookies cool on the baking sheet for about 15 minutes, then transfer them to a cooling rack to cool completely before frosting.