Preheat the oven to 375 degrees. Line 3 rimmed baking sheets with parchment paper; set aside.
In a large bowl, using an electric hand mixer, beat the butter, brown sugar, and granulated sugar for 2-3 minutes until light and creamy. Add eggs and vanilla and beat until well combined.
In a medium bowl, whisk together flour, cornstarch, baking soda, and salt. Add the dry ingredients to the wet ingredients, beating until just combined.
Gently stir in 1 1/2 cups of the graham cracker pieces, 1 1/2 cups of the marshmallows, and semisweet chocolate chips, stirring just until dispersed throughout the dough.
Using a large ice cream scooper, scoop 3 tablespoon size balls of dough onto the parchment-lined baking sheets, leaving room for the cookies to spread (6 cookies to a sheet).
Bake for 10 minutes until almost done, then remove from the oven and quickly press 4 additional marshmallows on top of each cookie, along with a 3 pieces of broken-up graham crackers and 2 mini-Hershey bars.
Turn the oven to broil and toast the marshmallows for about 1-2 minutes until golden brown. Watch careful as the marshmallows can burn quickly.
Cool for 2-3 minutes on the pan before transferring to a wire cooling rack. Store cooled cookies in an airtight container for 4-5 days.