Preheat the oven to 350 degrees Fahrenheit. Spray an 8x8-inch pan with non-stick cooking spray.
In a food processor, pulse the graham crackers until fine. In a small bowl, combine the crumbs, ¼ cup melted butter, and 2 tablespoons sugar. Press the mixture firmly in the bottom of the 8x8 dish.
In a medium bowl or KitchenAid mixer, whisk softened butter, 1 cup sugar, and cocoa until smooth. Add the eggs and stir.
Add the flour, vanilla, and salt until the mixture is combined. Spread half of the mixture over the graham cracker crust.
Sprinkle the marshmallows on top of the layer, then spread the remaining batter on top. Bake for 25 minutes.
Sprinkle the chocolate chips on top of the brownie. Return to the oven and bake for 3 more minutes.
Remove from oven and spread chocolate with a rubber spatula. Cool completely.