Basically Modan-yaki is a type of Okonomiyaki, Japanese savory pancake. Okonomiyaki is made from a batter containing flour, eggs and fish stock(dashi). Then, the batter is mixed with shredded cabbage and other ingredients such as pork belly, seafood(squid, cuttlefish, shrimp, and etc) and scallions.
In addition to these ingredients, modan-yaki includes either fried noodles(yakisoba) or udon noodles. With yakisoba is much popular than with udon noodles. Modan-yaki is similar to Hiroshima style Okonomiyaki but the difference is that Hiroshima style does not mix the ingredients together with the batter. Then, the batter itself does not contain eggs.
The name Modan-yaki comes from the English word "modern". May be at that time of the creation, Modan-yaki was a modern food for Japanese but it is funny that there is no western ingredients in it. If spaghetti is used instead of udon noodles, it should be modern.
Anyway, Modan-yaki is offered at all restaurants specialized in Okonomiyaki. Just be ready to choose which noodle to be included. Or may be some restaurants will automatically bring you with yakisoba noodles.