Beat softened butter in large bowl. Add brown sugar, granulated sugar, baking soda, and salt. Mix until combined. Next, beat in the eggs, vanilla, and flour. Stir in chocolate chips and crush 3 graham crackers to crumbs in a plastic bag, using a rolling pin. Cut marshmallows into 1/4's and add them in. Stir.
Separate the dough into 1 inch balls and stick a piece of graham crackers into each one for decoration. Place onto greased cookie pans.
Bake for 9-10 minutes or until the edges are lightly brown. Transfer cookies to a wire rack (cooling rack) to let it cool for several minutes.