Begin by cutting the cold butter into small pieces and add the butter to the bowl of a stand mixer.
Add the white sugar and brown sugar to the bowl as well, and beat until light and fluffy.
Add the eggs and vanilla extract to the sugar/butter mixture and beat again. Scrape down the sides of the bowl if necessary.
In a separate mixing bowl, sift or whisk together the all-purpose flour, cake flour, baking soda, and salt.
Add the flour mixture to the the wet ingredients and mix together.
Break the graham cracker sheets into bite-sized pieces and add them and the milk chocolate chips to the cookie dough. Stir together until combined.
Once the dough is mixed use a two-tablespoon cookie scoop to form a ball.
Use your thumb to make an indentation in the cookie dough ball. Place ½ of a jumbo marshmallow in the indentation and fold the dough around it while forming it back into a ball.
Place the cookie dough balls on baking sheet and refrigerate them for 30 minutes.
Preheat your oven to 375 degrees. Space the cookie dough balls on a parchment-lined baking sheet about 2 inches apart.
Bake the cookies for 8 minutes, then remove. Place one Hershey chocolate bar rectangle in the center of each cookie. Bake for an additional 2 minutes.
Remove from the oven and allow the cookies to rest on the baking sheet for 5 minutes, then transfer to a cooling rack.