Heat the oven to 325°F. Line the bottom and sides of a 9x13-inch baking pan with 2 sheets of parchment paper, arranging them perpendicular to each other so that the paper extends over all 4 sides by a few inches.

Arrange 15 of the chocolate graham cracker squares in a single layer in the bottom of the pan.

Prepare the batter from 1 (about 18-ounce) box brownie mix according to the package directions. Gently spread the brownie batter evenly on top of the graham crackers and smooth out the top.

Bake until a tester inserted into the center comes out clean, about 25 minutes. Place on a rack and let cool for at least 1 hour.

Whisk 3 cups room temperature heavy cream and 1 (5.9-ounce) package instant chocolate pudding mix together in a large bowl until smooth and combined. Fold in 1 cup of the thawed whipped topping with a flexible spatula until just combined. Spread the pudding mixture evenly over the brownies.

Beat 4 ounces room temperature cream cheese and 1 (about 7-ounce) jar marshmallow crème together in a stand mixer with the paddle attachment on medium speed until smooth and combined, about 30 seconds. Fold in the remaining whipped topping (about 2 cups) until just combined. Dollop and spread the mixture evenly over the pudding layer.

Arrange the remaining 15 chocolate graham cracker squares in a single layer over the marshmallow mixture. Cover and freeze until firm, at least 5 hours.

When ready to serve, grasp the excess parchment and transfer the slab onto a cutting board. Using the graham cracker squares as a guide, cut into 15 or 30 pieces.