Archiduc ice cream was a fancy ice cream preparation noted in New York City in the early 20th century. It was made by packing a hemispherical mold first with apricot ice cream, and then filling the middle with a praline of almonds and chestnuts. For other applications of hemispherical ice cream molds, see bombe glacée.
The connection to the haute cuisine term "archiduc" is obscure. The term is usually used to refer to dishes imagined to have an Austro-Hungarian basis, but no such connection is obvious here. There may be a connection to the famed apricots of Wachau, from Lower Austria.
Here is a recipe from 1916:
Ice cream "Archiduc"
Source: The Ice Cream Trade Journal, New York, June, 1916
Ice creams can, of course, be made of any desired form. A common method of preparing fancy ice creams is by lining an ordinary melon mold with one kind of frozen substance and placing in the center another substance which is either in frozen condition when so placed, or subsequently becomes chilled on packing the mold in ice and salt.
Outside, apricot ice cream; inside café pralinè, made in the following way : Almonds and chestnuts, or other nuts, are mixed with sugar, browned on the fire until the mass is caramelized. It is then cooled and made into a powder.