Heat a camping stove to medium (about 350° to 375°F), or fit a grilling grate over the direct heat of glowing embers. Tear or cut 8 (12-inch) squares of aluminum foil. Crumple each foil square into a 2-inch ball. Flatten each slightly, and arrange on bottom of a 7 ½ quart cast-iron Dutch oven. Cover with the lid, and preheat on the camping stove or grilling grate directly over the heat source 10 minutes. Reduce the heat to medium-low (about 300° to 325°F).
Line the bottom and sides of a 9- x 2-inch round cake pan with 2 layers of aluminum foil, allowing the foil to extend about 1 inch above the rim of the cake pan. Fold the edges of the foil to extend about 1 inch above the rim of the cake pan. Fold the edges of the foil down to create an even ½ - inch collar above the rim of the pan. Coat the foil with cooking spray.
Finely crush 4 graham crackers in a plastic freezer bag. Stir together the crushed graham crackers, cookie mix, butter, and egg until a soft dough forms. Press the dough into the prepared cake pan. Using togs, lower the pan onto the foil balls in the Dutch oven, Cover and cook on the camping stove over medium-low until a knife inserted in the center comes out clean and the edges are golden, about 1 hour. Remove the Dutch oven from the heat.
Sprinkle the chocolate chips evenly over the top of the cookie in the Dutch oven; top evenly with the marshmallows. Cover with the lid, and let stand 10 minutes or until the chocolate melts and the marshmallows slightly soften. Coarsely crush the remaining 2 graham crackers, and sprinkle over the marshmallows. Lift the cookie out of cake pan using the foil collar as handles; cut into 10 wedges.