Prep: Place marshmallows on parchment-lined tray and freeze. Finely grind 4–5 graham sheets into powder. Coarsely crush 2–3 more sheets for topping. Break Hershey's bars into small pieces. Set all aside.
Brown butter: In saucepan over medium heat, melt butter. Cook, stirring, until amber with brown specks and nutty. Pour into large bowl. Cool 15–20 minutes.
Mix wet: Add brown sugar and granulated sugar to cooled butter. Whisk until glossy. Add egg and vanilla. Whisk vigorously 1–2 minutes until pale, thick, and forms ribbons.
Mix dry: In separate bowl, whisk together flour, finely ground graham crumbs, baking soda, and salt.
Combine: Add dry ingredients to wet. Fold with spatula until just a few flour streaks remain.
Add chocolate: Fold in chocolate chips until evenly distributed.
Stuff and shape: Scoop 50g dough portions. Flatten in palm. Place frozen marshmallow in center. Wrap dough completely around marshmallow, sealing tightly. Roll into smooth ball.
Freeze: Place stuffed dough balls on parchment-lined tray. Freeze at least 4 hours until solid.
Preheat and prep: When ready to bake, preheat oven to 180°C (355°F). Line baking sheets with parchment.
Bake: Place frozen dough balls on prepared sheets, 3–4 inches apart. Bake 13–15 minutes, rotating halfway, until edges golden and centers soft.
Add toppings: Immediately out of oven, press Hershey's pieces and coarse graham chunks onto each warm cookie.
Cool: Let cookies rest on baking sheet 8–10 minutes. Transfer to wire rack to cool completely or serve warm.
