Line a 9 by 5-inch loaf pan with plastic wrap.
Place the softened ice cream into the loaf pan and spread evenly.
Place the piece of cake on top of the ice cream, press down lightly, and place the pan in the freezer for 1 hour.
After an hour, combine the sugar, corn syrup, and water in a 2-quart saucepan and place over high heat. Stir just until the sugar dissolves, about 5 minutes. Clip on a candy thermometer and bring the mixture to 240 degrees F.
While the syrup is cooking, place the egg whites, salt, and vanilla into the bowl of a stand mixer and, using the whisk attachment, whisk the eggs on high speed until they reach medium peaks, 4 to 5 minutes.
When the sugar syrup reaches 240 degrees F, remove from the heat and, with the stand mixer on low speed, slowly and carefully pour the syrup in a thin steady stream into the egg white mixture, being careful not to come in contact with the whisk. Once all the syrup has been added, increase the mixer speed to high and whisk until stiff peaks are formed and the mixture has cooled, 8 to 10 minutes.
Remove the loaf pan from the freezer, turn upside down onto a heatproof serving platter, and remove the plastic wrap. Completely cover the ice cream cake combo with a 1-inch layer of meringue all around, sealing the meringue to the pan around the bottom edge.
Use a propane torch to brown the meringue all over. Serve immediately. May be frozen once the meringue has browned.
Propane Gas Torch Safety: Propane gas torches are highly flammable and should be kept away from heat, open flame, and prolonged exposure to sunlight. They should only be used in well-ventilated areas. When lighting a propane gas torch, place the torch on a flat, steady surface, facing away from you. Light the match or lighter and then open the gas valve. Light the gas jet, and blow out the match. Always turn off the burner valve to "finger tight" when finished using the torch. Children should never use a propane gas torch without adult supervision.
Recipe courtesy Alton Brown, 2010