Preheat oven to 350° F. Lightly grease bottom of a 9×9-inch baking pan with butter or shortening.
In medium saucepan, melt the butter and chocolate over very low heat, stirring constantly. Remove from heat and stir in sugar, eggs and vanilla. Mix in flour, just until combined.
Spread half of the batter in the prepared baking pan. Sprinkle the broken graham crackers over the batter. Top the graham cracker layer with marshmallows. Spread the remaining batter on top of the marshmallows and graham crackers, cover them completely.
Bake for 25 minutes, or until set. Cool completely, about 1 hour. Cut into 4 rows by 4 rows to make 16 brownies.