I was mystified by the German Schichttorte in the Great British Bakeoff programme, but then I realized they meant Baumkuchen.
I think the word Schichttorte is a misnomer. Any cake with layers is a Schichttorte, and it will usually have buttercream between the layers, like an opera cake. Whereas the cake they showed consisted simply of twenty layers of sponge cake, each grilled separately as they were built up, with no filling but with a coating.
The programme did show a real Baumkuchen being made: the cake mixture is dripped onto a sort of metal spit revolving on a grill. Here are pictures from the LA Times. you can buy one from the German Bakery in Windsor.
The cake in the program was grilled layer by layer in a cake tin, but it was still a Baumkuchen in structure, although the layers run in a different direction.
By chance I am more familiar with the Transylvanian Baumstriezel. It is also made on a rotating tube, but the pastry contains yeast and it is covered with caramelized sugar. It is apparently the Hungarian Kürtőskalács.
Meanwhile, the Japanese besieged Qingdao in World War I and thus inadvertently introduced a Baumkuchen maker to Japan.
Baumkuchen is one of the most popular pastries in Japan, where it is called baumukūhen (バウムクーヘン?). It is a popular return present in Japan for wedding guests because of its typical ring shape.
It was first introduced to Japan by the German Karl Joseph Wilhelm Juchheim. Juchheim was in the Chinese city of Tsingtao during World War I when Britain and Japan laid siege to Tsingtao. He and his wife were then interned at Okinawa. Juchheim started making and selling the traditional confection at a German exhibition in Hiroshima in 1919. After the war, he chose to remain in Japan. Continued success allowed him to move to Yokohama and open a bakery, but its destruction in the 1923 Great Kantō earthquake caused him to move his operations to Kobe, where he stayed until the end of World War II. Some years later, his wife returned to help a Japanese company open a chain of bakeries under the Juchheim name that further helped spread baumkuchen’s popularity in Japan.