Preheat the oven to 325ºF. Spray a Baker’s Edge nonstick brownie pan or 9-by-13-inch pan with nonstick baking spray. Set aside.
Crush the graham crackers into a fine powder and stir in the sugar and salt. Add the butter and stir until combined. Press the graham cracker crust in an even layer into the pan.
In a small bowl, whisk together the cocoa powder, flour, salt, and baking powder.
In a heavy-bottomed saucepan, combine the butter, both sugars, the bittersweet chocolate, coffee, and vanilla. Stir continuously over low heat until the butter, sugars, and chocolate have completely melted and slightly thickened. Remove from the heat while continuing to stir for 30 seconds to dissipate some of the heat.
Whisk the egg in a small bowl and add a small amount of the hot melted chocolate mixture to the egg while whisking constantly to keep the egg from cooking. Add this mixture to the remaining chocolate mixture, whisking until the egg is incorporated. Sift the cocoa/flour mixture over the melted chocolate mixture and stir until smooth. Pour the brownie mixture over the graham cracker mixture and bake for 20 to 25 minutes or until a toothpick inserted into the brownie comes out with only a few moist crumbs.
Remove the brownies from the oven and increase the heat to broil. Sprinkle the tops of the brownies with the mini marshmallows and brown under the broiler for a few seconds.