Preheat the oven to 350 degrees F. Make the large graham crackers: Discard 3/4 cup of the cookie mix. Prepare the remaining mix as directed for cut-out cookies, adding the ground graham crackers.
Divide the dough in half. Roll out each piece of dough into a 9 1/2-inch square on separate sheets of parchment paper; transfer the dough and parchment to 2 baking sheets.
Bake the graham-cracker cookies until golden and set, 12 to 15 minutes. While still warm, trim the edges with a paring knife to make even 9-inch squares.
Use a butter knife to score a perforated line across the middle of each cookie, then use a chopstick or skewer to make small holes as shown. Let cool completely.
Using an offset spatula, spread the fudge sauce into a wavy pool on 1 cookie. Transfer to the freezer.
Let the ice cream soften slightly, then cut off the carton and place the block of ice cream on its side on a piece of plastic wrap. Cover with more plastic and press the ice cream to flatten slightly. Freeze until firm, about 1 hour.
Meanwhile, make the meringue: Beat the egg whites and cream of tartar with a mixer on medium-high speed until foamy, then gradually beat in the sugar on high speed until stiff glossy peaks form.
Remove the plastic and set the ice cream on top of the fudge-covered cookie. Using an offset spatula, cover the ice cream with a smooth layer of meringue, building out the sides slightly.
Use a kitchen torch to brown the meringue, then gently press the other graham-cracker cookie on top. Freeze until ready to serve, then let soften slightly and slice.