Preheat oven to 350 degrees F. Line an 8-inch baking pan with foil.
In a large glass bowl, place butter and chocolate. Heat in microwave at full power for about 1 minute or just until butter is melted. Remove from microwave and stir until smooth.
Stir sugar into butter-chocolate mixture. Add eggs, one at a time, beating with a wooden spoon after each one. Stir in vanilla, flour and salt; mix well. Fold in marshmallows and chocolate chips.
Spread half of the batter in pan. Crush 2 graham cracker sheets with your hands. Sprinkle evenly on top of batter. Carefully spread the rest of the batter over the crackers (don’t worry if you don’t cover up all the cracker). Crush up the last cracker and sprinkle on top.
Bake brownies for 25 minutes. Cool completely on a wire rack before cutting into squares.
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