Beat the butter, shortening and sugar until light and fluffy, about 1-2 minutes.
Add the egg, egg yolk 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 and may overspread.
Fold in the chocolate chips and the crumbled graham crackers and refrigerate for at least one hour.
Preheat the oven to 350°F. Roll the dough into 1 inch balls and smash into a flat disk. Place ½ 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 the dough balls 2 inches apart on baking sheet and bake for 10-12 minutes, until edges are golden brown.
Let the cookies cool for 10-15 minutes on baking sheet (until completely cool) then transfer to rack to cool completely.
Notes
Don't over mix the dough as it will cause the cookies to be tougher. It's ok if there are a few streaks of flour.
Use broken chocolate bars instead of chocolate chips for a more rustic look.
You can substitute mini marshmallows for the full marshmallows. Just mix them in with the batter.
Make the dough the day before if you want to save some time.
Line the baking sheet with parchment paper to avoid cleanup and help keep the cookies from sticking.
Let the cookies cool completely before removing them from the baking sheet.