Beat the butter, shortening and sugar until light and fluffy, about 1-2 minutes.
Add the eggs and vanilla and beat for another minute.
Combine the dry ingredients (flour, baking soda, salt) in a separate bowl.
Combine the wet and dry ingredients, mixing until the flour is just barely streaking through. Don't over mix or your cookies will be tough.
Fold in the chocolate chips and the crumbled graham crackers and refrigerate for at least one hour. Typically, I make the dough the night before so I can go straight into cookie making the next day.
Preheat the oven to 350 degrees. Roll the dough into 1 inch balls and smash into a flat disk. Place 1/2 of a marshmallow on the dough and roll the dough up around the marshmallow.
Press together and seal the edges. It's ok if a little marshmallow shows through.
Place 2 inches apart on baking sheet and bake for 10-12 minutes, until edges are golden brown.
Let the cookies cool for 5 minutes on baking sheet then transfer to rack to cool completely.