Preheat oven to 350°F (175°C). Grease a 9×13-inch baking dish.
In a large bowl, combine chocolate cake mix, water, eggs, and oil. Beat with an electric mixer on medium speed until smooth, about 2 minutes.
Pour batter into prepared dish and bake until a toothpick inserted into the center comes out clean, 26–30 minutes.
Let cake cool completely on a wire rack.
Meanwhile, remove ice cream from its carton. Place block on its side and use a string or dental floss to cut it in half lengthwise. Place the slabs side by side on waxed paper.
Carefully remove cooled cake from the baking dish and place over the ice cream slabs. Trim edges so they align neatly.
Place a serving platter or board over the cake. Holding both the platter and wax paper, flip the cake over. Remove wax paper and smooth the seam between ice cream slabs.
Cover the top with waxed paper and freeze until very firm, at least 4 hours.
Decorate as desired with whipped cream, sprinkles, or chocolate shavings before serving.