Preheat oven to 350 degrees F. Line a 11x7x1 1/2-inch baking pan with parchment paper or lightly grease the pan. Set pan aside.
In a medium saucepan melt the butter and chocolate over low heat. Remove from heat. Stir in sugar, eggs, and vanilla until combined. Stir in flour.
Spread half the batter in the prepared pan. Top with graham crackers (divide as needed to evenly top the batter). Sprinkle marshmallows on the graham crackers, but do not let them touch the sides of the pan. Carefully spread the remaining batter on the marshmallows and graham crackers, covering them completely.
Bake brownies for 25 minutes or until set. Cool completely on a wire rack. Cut into bars.