Hiyashi Tororo Soba is cold soba noodles served in a bowl, with a bowl on the side that has in it puréed Yamaimo (aka Japanese Mountain Yam), and a raw egg. You pour the puréed yam into the noodles and stir it all up to eat it.
Yamaimo
Imokake Soba Noodles
Imokake Soba is kake soba topped with grated Yamaimo (Japanese Mountain Yam), and a raw egg. See entries on kake soba and Yamaimo for more information.
Jinenjo Soba Noodles
Jinenjo Soba are soba noodles made from buckwheat, wheat and jinenjo flour (aka old Yamaimo flour.) They are usually served in a hot broth, or they can be used as a fried noodle.