Line an 8x8x2-inch baking pan with aluminum foil or parchment paper. Spray with nonstick cooking spray. Set aside.
In a medium saucepan, melt butter and chocolate. Remove from heat and add in the eggs, sugar and vanilla. Beat in the flour until just combined.
Spread half the batter in the prepared pan. Top with graham crackers (divide as necessary to evenly top 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 for 25 to 27 minutes or until set. Cool completely on a wire rack. Cut into bars. Makes 16 brownies.