Preheat the oven to 350 degrees.
Use a food processor to crush the graham crackers to fine crumbs. Combine the flour, graham crackers, baking powder, and salt together in a bowl; mix well.
Beat the butter with the sugars until creamy and smooth. Add the egg and vanilla and beat until well combined. Slowly add the flour mixture to the butter mixture until just combined. Add the marshmallow bits and chocolate chips and mix.
Place spoonfuls of cookie dough onto a baking sheet about 2 inches apart. Place into the oven and bake for 10-12 minutes or until golden brown. Let the cookies cook for a couple of minutes before moving them to a cooling rack. Enjoy dipped in ice cold milk.