Preheat oven to 350F. Line an 9-by-10-inch baking pan with parchment paper so the edges of parchment paper stick up (this way you can lift the bars out to cut when they are done); set aside.
In a large bowl, mix the brown sugar, eggs, and vanilla.
Pour the melted butter into the brown sugar mixture and whisk until smooth. (make sure the melted butter isn’t very hot, or it may cook the eggs)
Add the flour, baking powder and salt and stir until just combined, don’t overmix.
Fold in the crushed graham crackers, marshmallows and chocolate.
Spread the batter out into prepared pan, smoothing the top lightly with a spatula.
Bake for about 20 to 25 minutes, or until bars have firmed up in the center and edges are set. The center will still be gooey, but not raw and some of the marshmallows will have a slight golden color.
Allow bars to cool in pan for at least 30 minutes, then transfer to the fridge for another 20 minutes before cutting.
Cut the cooled bars into squares and serve topped with extra marshmallows and Hershey bar pieces.