Preheat the oven to 350 degrees F. Coat two 12-by-17-inch rimmed baking sheets with cooking spray, then line with parchment paper, leaving an overhang on the short sides.
Prepare the cake mix with an extra egg. Divide the batter between the 2 baking sheets; spread evenly with an offset spatula. Bake until set, 8 to 9 minutes; let cool.
Measure 2 1/2 inches in from each long side of one cake; mark with toothpicks. Score using a ruler, then remove the toothpicks and trim along the scored lines so the cake is 7 inches wide.
Round the corners of the cake with a knife. Punch out holes with a straw (4 holes across, 10 down). Trim the other cake (no need to punch holes). Freeze the cakes 30 minutes.
Invert the cake without the holes onto a clean baking sheet; peel off the parchment. Snip open 1 ice cream carton with kitchen shears, then slide the ice cream onto the cake.
Repeat with the other 2 cartons of ice cream, arranging them side by side on the cake. Cover with plastic wrap and press with your hands to smooth the ice cream and fill the gaps.
Remove the other cake from the parchment with a thin spatula; place it on the ice cream. Trim any excess cake and smooth the sides. Freeze at least 2 hours before serving.
Photograph by Andrew Purcell
Recipe courtesy Food Network Magazine