Preheat the oven to 350°F. Grease a 9×13-inch baking pan, then line it with foil, leaving some overhang on the sides. Lightly grease the foil.
Make the graham cracker crust. In a medium bowl, combine 3 cups graham cracker crumbs and 1/4 cup granulated sugar. Add 3/4 cup melted butter and stir with a fork until the crumbs are evenly moistened.
Press the graham cracker mixture firmly and evenly into the bottom of the prepared pan.
Bake the crust for about 15 minutes, or until lightly golden brown.
While the crust bakes, prepare the 9×13-inch brownie mix according to the package directions.
Remove the crust from the oven and carefully spread the prepared brownie batter evenly over the warm crust.
Bake according to the brownie mix package directions, until the brownies are set and a toothpick inserted into the center comes out with a few moist crumbs.
Remove the brownies from the oven and switch the oven to broil. Immediately spread one 10-ounce bag of mini marshmallows evenly over the top.
Place the pan under the broiler for 1 to 2 minutes, watching closely, until the marshmallows are puffed and lightly toasted. Do not walk away, as they can burn quickly.
Remove the pan from the oven and immediately press broken graham cracker pieces gently into the warm marshmallow layer.
Let the brownies cool completely in the pan before lifting them out using the foil overhang.
Cut into squares and serve. Store leftovers in an airtight container at room temperature.