Preheat the oven to 350 degrees. Line a baking sheet with parchment paper.
In a large bowl cream together sugar and butter. Add egg and vanilla, mix well.
Add dry ingredients and combine until a soft dough forms.
Finally add chocolate chips, the frozen marshmallows (reserve a handful) and graham crackers. Mix well.
Using a cookie scoop or a spoon, drop 2 tbsp sized balls of dough onto a greased or parchment lined cookie sheet. Top each with a few frozen marshmallow halves.
Bake for 10-12 minutes or until the edges start to brown.
If the cookies have a marshmallow, caramel explosion, use a round cookie cutter or butter knife to quickly press them back into a uniform cookie shape.
Transfer baked cookies to a cooling rack.