Preheat oven to 375 degrees F. Line two baking sheets with parchment paper.
In a large mixing bowl, combine butter, brown sugar, and granulated sugar. Beat for 2-3 minutes until creamy.
Add eggs and vanilla and beat well until incorporated.
Add flour, cornstarch, baking soda, and salt, mixing just until combined.
Add 1 1/2 cups of the graham cracker pieces, 1 1/2 cups of the marshmallows, milk chocolate chips, and semisweet chocolate chips, stirring just until dispersed throughout the dough.
Scoop 2-3 tablespoon size balls of dough onto the parchment lined baking sheets, leaving room for the cookies to spread. Bake for 10 minutes until almost done, then remove from the oven and press 4-5 additional marshmallows on top of each cookie, along with a couple extra pieces of broken-up graham cracker and Hershey bar.
Return to oven and bake for 1-2 minutes until done. If desired, switch oven to broil and toast the marshmallows on top. But be careful as the small marshmallows can burn quickly.
Cool for 2-3 minutes on the pan before transferring to a wire cooling rack. Store in an airtight container on the counter for 4-5 days.