Prep: Preheat oven to 350°F. Line a 9x9 pan with parchment paper on all sides.
Graham crackers: In the bottom of your lined pan, arrange a single layer of graham crackers. You might need to cut some of the graham crackers into smaller pieces to fit into the pan. Set aside.
Chocolate: To a medium bowl, add chopped chocolate, cocoa powder, and espresso powder. Set aside.
Brown the butter: In a medium pan, heat the butter on medium heat. Shortly after it has melted, the white milk solids will start to separate out and it will start to fizz and bubble. Stir occasionally. When the fizzing slows down, it will start to foam. Keep stirring and keep watching at this point because the milk solids will brown very quickly. Once the milk solids are golden brown and the butter smells nutty, immediately remove it from the heat.
Melt chocolate: Pour the browned butter into your bowl of chocolate to bloom the cocoa powder. Stir the mixture until the chocolate has melted. Set aside to cool for at least 10-15 minutes while you mix the rest of the batter.
Mix the batter: In a large mixing bowl, add the eggs, granulated sugar, and brown sugar. Whisk them together for about 2 minutes until thoroughly mixed. Slowly stream in the chocolate mixture while whisking at the same time and all combined. Add the flour and fold together until just combined.
Fill pan: Pour the brownie batter into your pan on top of the graham cracker layer. Spread it into the corners of the pan by shaking the pan or smoothing it with an offset spatula.
Bake: Bake for about 28-30 minutes or until the edges are set and a toothpick inserted in the middle comes out mostly clean but with some wetness.
Broil marshmallows: Immediately after taking the brownies out of the oven, move the oven rack to the top of the oven. Arrange a layer of marshmallows on top of the brownies. Return the pan to the oven and turn on the broiler. Broil the marshmallows for 2-3 minutes or until they're toasted to your liking. Watch them the entire time as they will toast (and burn) very quickly!
Cool: Let the brownies cool in the pan on a wire rack for at least 30 minutes before lifting them out of the pan by the parchment paper overhang. Let the brownies cool on a wire rack completely before slicing. I usually stick them in the fridge after about an hour to cool them down faster.
Slice: To release the marshmallow layer from the parchment paper, rub a bit of cooking oil on an offset spatula or knife and run it in between the marshmallow layer and the parchment paper. When slicing, rub a bit of cooking oil on your knife to prevent the marshmallows from sticking to the knife.