Prep: Preheat your oven to 350°F (175°C). Line a 9x9-inch baking pan with parchment paper, making sure it covers all sides and leaves an overhang for easy removal.
Graham Cracker Layer: Arrange a single layer of graham cracker squares along the bottom of the prepared pan. You may need to trim some pieces to ensure full coverage. Set the pan aside.
Prepare the Chocolate Mixture: In a medium heatproof bowl, combine the chopped chocolate, natural cocoa powder, and espresso powder. Set aside—this mixture will be melted with the browned butter shortly.
Brown the Butter: In a medium saucepan over medium heat, melt the unsalted butter. As it melts, it will begin to bubble and fizz while the milk solids separate. Stir occasionally. Once the bubbling slows, the butter will begin to foam. Keep stirring until the milk solids turn golden brown and release a nutty aroma. Immediately remove from heat to prevent burning.
Melt the Chocolate: Pour the hot browned butter over the bowl of chocolate and cocoa. Stir until everything is melted and the mixture is smooth and glossy. Let it cool for 10–15 minutes before proceeding to avoid scrambling the eggs in the next step.
Make the Batter: In a large mixing bowl, whisk together the eggs, granulated sugar, and brown sugar for about 2 minutes, until well combined and slightly frothy. While whisking continuously, slowly stream in the cooled chocolate-butter mixture until fully incorporated. Add the all-purpose flour and gently fold it into the batter until just combined—do not overmix.
Assemble: Pour the brownie batter over the graham cracker layer in your pan. Smooth the top with an offset spatula or gently shake the pan to level the surface.
Bake: Place the pan in the oven and bake for 28–30 minutes, or until the edges are set and a toothpick inserted into the center comes out with moist crumbs but no raw batter.
Add Marshmallows and Broil: Once the brownies are baked, remove the pan from the oven and move the oven rack to the top position. Arrange a single, even layer of large marshmallows (about 36) over the hot brownie surface. Place the pan back in the oven and broil for 2–3 minutes, or until the marshmallows are golden brown and toasted to your liking. Watch carefully—they can burn in seconds under the broiler.
Cool: Allow the brownies to cool in the pan on a wire rack for at least 30 minutes. Use the parchment paper overhang to lift them out of the pan, and let them cool completely on the wire rack. For cleaner slices, you can refrigerate them after an hour to firm them up.
Slice and Serve: To prevent the marshmallow topping from sticking, lightly grease a knife or offset spatula with oil. Gently slide it between the marshmallow layer and the parchment to release. When slicing, re-grease the knife as needed to get clean, neat cuts.