Preheat the oven to 375°F (190°C).
Add both types of sugar and room temperature butter into a mixing bowl. Beat for about 1-2 minutes until well-combined. You can use a hand mixer or a stand mixer fitted with a paddle-shaped attachment.
Add the egg and vanilla extract. Beat for 1-2 minutes or until well-combined.
Stir the flour with baking soda, graham cracker crumbs, and salt in a small bowl. Add the flour mixture to the mixing bowl. Mix over low speed until half-combined (the flour shouldn’t be fully incorporated at this point).
Add the chocolate chips (or roughly chopped chocolate) and 2 whole graham crackers crumbled into smaller pieces to the mixing bowl (set the third graham cracker aside).
Mix until the chocolate and cookie pieces are evenly distributed and there are no streaks of flour visible.
Scoop the dough with a 3 Tbsp scoop (generously), flatten it out in your hand, put 5-6 mini marshmallows in the middle (or 1/2 of a large marshmallow). Wrap the cookie dough around marshmallows forming a ball of dough. The marshmallows should not be visible. Repeat with the remaining dough and marshmallows.
Place the cookies at least 2 inches (5 cm) apart on a baking sheet lined with parchment paper. Top the cookies with 3 small pieces of the remaining graham cracker.
Bake for 11-12 minutes. The cookies will be still soft (they will finish baking on the sheet pan) and should be golden at the edges. Leave them on the baking sheet to cool.
Enjoy!