Barney notes the Baked Alaska they are served during the club dinner - Baked Alaska is unique in that's it's the only dish made with ice cream that's actually baked in an oven. Baked Alaska (also known as glace au four, omelette à la norvégienne, Norwegian omelette and omelette surprise) is a dessert made of ice cream placed in a pie dish lined with slices of sponge cake or Christmas pudding and topped with meringue. The entire dessert is then placed in an extremely hot oven for just long enough to firm the meringue. The meringue is an effective insulator, and in the short cooking time needed, it prevents the heat from getting through to the ice cream.
Barney actually wasn't that far off when he said it was a new dessert they came up with since Alaska became a state. This dessert was first called "Baked Alaska" in 1876 when Delmonico's Restaurant in New York City named it in honor of the newly acquired territory of Alaska.