This famous tako-yaki (octopus dumplings) stand, just north of Dōguya-suji arcade, uses custom copper hotplates (instead of cast iron) to make dumplings that are crisper than usual (but still runny inside). There's a picture menu and tables and chairs in the back. One popular dish to try is tako-sen – two dumplings sandwiched between sembei (rice crackers).
There's also a convenient branch in Ame-Mura.