Not really a 限定 (limited offering), but Hototogisu in Hatagaya becomes Ura (opposite) on Thursdays.
The soup is made with three kinds of niboshi, and the line is always long.
This was great, but I wasn't blown away. I absolutely love their regular bowl, though. So I'm going to be all ura myself and say that the rest of the week is better.
My original (very old) review of Hototogisu is here.