Preheat oven to 350°F and line baking sheets with parchment paper.
Cream together butter, brown sugar, and granulated sugar until fluffy, about 2-3 minutes.
Add eggs and vanilla extract, beating until well combined.
In a separate bowl, whisk together flour, graham cracker crumbs, baking soda, and salt.
Gradually mix dry ingredients into wet ingredients until just combined.
Fold in chocolate chunks, mini marshmallows, and broken graham cracker pieces.
Scoop 2-tablespoon portions of dough onto prepared baking sheets, spacing 3 inches apart.
Bake for 9 minutes, then quickly remove from oven and press a marshmallow half onto the center of each cookie.
Return to oven and bake for an additional 2 minutes until marshmallows are slightly puffed and golden.
Let cool on baking sheet for 5 minutes before transferring to a wire rack. The marshmallows will settle as they cool.