Preheat your oven to 350 degrees F and line a 9x9-inch pan with parchment paper, making sure the paper hangs over the sides for easy removal.
Place graham crackers on the bottom of the lined pan, breaking them if needed to fit.
In a medium-sized saucepan, melt the butter over medium heat. Once melted, remove from heat and stir in the sugars. Let the mixture cool for about 5 minutes.
Whisk the eggs and vanilla into the butter and sugar mixture. Add the cocoa powder and gently fold in the flour, baking powder, and salt until just combined
Pour the batter over the graham crackers in the pan and bake for approximately 30 minutes.
After 30 minutes, take the pan out of the oven and sprinkle the chopped chocolate over the top. Allow the chocolate to sit for a few minutes, then use a small offset spatula to spread it evenly over the brownies.
Arrange the marshmallows on top in rows and return the pan to the oven for an additional 5 minutes.
Once the marshmallows are slightly toasted, either use a kitchen torch to further toast the tops or place the pan on the top rack of your oven and broil for 15-30 seconds.
Let the brownies cool for about 20-30 minutes before cutting them into squares. Enjoy!