Prepare the Brown Butter:

 In a saucepan over medium to low heat, brown the butter. This takes about 5 to 10 minutes. Once it has a nutty aroma and you see brown specks, immediately remove from heat and transfer into a baking dish. Let this cool for 10 minutes.

Mix the Sugars and Wet Ingredients:

In a large mixing bowl, combine the cooled brown butter with the brown sugar and granulated sugar. Mix until completely cohesive, about 2 minutes. Add the egg, egg yolk, and vanilla extract, and mix well.

Combine the Dry Ingredients:

In a separate bowl, whisk together the all-purpose flour, graham cracker crumbs, baking soda, cornstarch, and salt. Gently fold the dry mixture into the wet mixture until just combined.

Add the Mix-Ins:

Fold in the chocolate chips, mini marshmallows, and graham cracker pieces until evenly distributed throughout the dough.

Scoop and Chill the Dough:

Using a cookie scoop, portion the dough onto a lined baking sheet. Refrigerate for 30 minutes. (Chilling after scooping prevents the dough from hardening too much, making it easier to handle.)

Bake the Cookies:

Preheat your oven to 350°F (175°C). Bake the cookies for 12 to 14 minutes, or until the edges are golden brown and the centers are set. Let cool on the baking sheet for 15 minutes before transferring to a wire rack to cool completely.