Whisk together the flour, cornstarch, baking soda, and salt in a medium bowl. Set aside.
In a large mixing bowl, beat the cold butter, granulated sugar, and light brown sugar until creamy and well combined.
Add the eggs one at a time. Mix in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients. Mix just until a thick cookie dough forms.
Divide the dough into nine portions weighing approximately 4 ounces each.
Flatten one portion of dough in your hand. Place chocolate chunks, graham cracker pieces, and one large marshmallow in the center.
Bring the dough around the filling and seal it completely. Do not allow the marshmallow to poke through any part of the dough.
Repeat with the remaining balls of dough.
Refrigerate the stuffed cookie dough balls for at least 30 minutes or cover and chill overnight.
Preheat the oven to 375°F. Line a baking sheet with parchment paper.
Place the cold cookie dough balls several inches apart on the prepared baking sheet.
Bake for 15 to 18 minutes, until the edges are golden brown and the centers are still slightly soft.
Let the cookies cool on the baking sheet for 10 minutes before transferring them to a cooling rack.
Add flaky sea salt while the cookies are warm, if desired.