In a medium saucepan over medium heat, melt the butter and semi-sweet chocolate, stirring constantly, about 5 minutes. Or melt in a medium microwave safe bowl in 30 second increments until melted and smooth.
Remove from the heat, pour into a large mixing bowl and allow to cool slightly for 8-10 minutes.
Adjust the oven rack to the lower third position and preheat the oven to 350°F.
Line a 9x9 inch square baking pan with aluminum foil or parchment paper, leaving an overhang on all sides to remove the brownies easily after baking.
Once the chocolate and butter are cooled slightly, whisk in the granulated and brown sugar.
Add the eggs, one at a time, whisking until smooth after each addition.
Whisk in the vanilla then gently fold in the flour, cocoa powder, and salt. Be careful not to overmix.
Pour half of the batter into the prepared baking pan.
Place the chocolate bars on top of the batter to cover the whole thing. You may need to break pieces to make them fit. It’s okay if there are spaces in between.
Pour the other half of the batter on top of the chocolate bars and smooth to even out the batter.
Gently sprinkle the graham cracker crumbs on top.
Bake for 35-36 minutes, or until the brownies begin to pull away from the edges of the pan.
Remove brownies from the oven and top with marshmallows.
Return to the oven and continue to bake for an additional 3 minutes.
Marshmallows will warm and puff up (almost double in size). If the marshmallows aren't toasted enough, turn on your broiler for 1-2 minutes, being careful not to overbake.
Remove from oven and allow the brownies to cool completely in the pan set on a wire rack.
Once cooled, lift the foil out of the pan using the overhang on the sides and cut into squares.