Prepare the Pan: Start by adjusting your oven rack to the middle position and preheating the oven to 350°F (180°C). I always take a moment to line my 8-by-8-inch baking pan with two wide strips of aluminum foil, making sure there is about three inches of overhang on all sides. This creates a "sling" that makes it so much easier to lift the whole block of brownies out later. Once the foil is in place, give it a good spray with nonstick cooking spray so that your gooey marshmallows don't cling to the sides when you are ready to serve.
Make the Graham Cracker Crust: Break your graham crackers into small pieces and pulse them in a food processor until they are finely ground into crumbs. In a small microwave-safe bowl, melt 4 tablespoons of butter, then stir it into the crumbs along with a tablespoon of sugar and a quarter-teaspoon of salt. Scrape the mixture into your pan and use a flat-bottomed glass to press it down firmly into an even layer. I like to make sure the crumbs are really packed tight across the bottom and slightly up the sides so the crust doesn't crumble apart when you go to slice it later.
Melt the Chocolate and Butter: In a large microwave-safe bowl, combine your bittersweet chocolate and the remaining 8 tablespoons of butter. Microwave the mixture on high in 30-second bursts, making sure to stir it well each time until it is completely melted and looks perfectly smooth and glossy. I always keep a close eye on this part because you don't want the chocolate to get too hot and burn. Once it’s fully melted, let it sit for a minute to cool down slightly before you start adding the rest of your brownie ingredients into the bowl.
Mix the Brownie Batter: Whisk in the remaining half-cup of sugar, the eggs, espresso powder, vanilla, and the rest of the salt until the mixture is thick and well combined. Add in your flour and baking powder, and give it one last whisk until the batter is velvety and smooth without any white streaks. The espresso powder is my favorite part because it really deepens the flavor of the chocolate without making the brownies taste like coffee at all. Pour this rich batter over your graham cracker crust and use a spatula to smooth it out into a nice, even layer.
Bake and Top with Marshmallows: Slide the pan into the oven and bake for about 25 to 30 minutes. You’ll know they are ready when a toothpick inserted into the center comes out with just a few moist crumbs attached. Once you take the pan out, immediately move it to a wire rack and pour those three cups of mini marshmallows over the top while the brownies are still hot. Try to spread them out as evenly as possible so that every square inch of the chocolate is covered by a little white marshmallow cloud.
Broil and Cool: Move your oven rack to the upper third position and turn on the broiler. Place the brownies back in the oven for just about one minute, watching them like a hawk, until the marshmallows are perfectly golden brown and toasted. This happens very fast, so stay right there and don't walk away! Let the brownies cool in the pan for at least an hour at room temperature before you try to slice them. I find that lightly greasing my chef's knife with cooking spray makes it much easier to cut through those sticky marshmallows for a clean, beautiful serving.
