Heat sugar and butter in a medium pot over low heat until butter is completely melted, stirring often. Remove from heat, stir in 1 1/2 c. chocolate chips until melted, and let cool to room temperature.
In a small bowl, briefly whisk the eggs. Add 1 to 2 tablespoons of chocolate mixture to the eggs and stir to combine, just to temper the eggs. Then pour all of eggs into the pot with the melted chocolate. Stir to combine.
Stir in flour, vanilla and baking soda until well blended. Pour into a greased 13×9 casserole dish.
In a small bowl, combine the graham crackers and butter and sprinkle over the brownies. Add the marshmallows and the chocolate pieces.
Bake at 350 degrees for 18 to 22 minutes.
