Nagaimo: I used nagaimo (2 inch segment), peeled, sliced (1/4 inch) and cut in half rounds.
I put a pat of butter (1 tsp) in a frying pan on medium low flame. When the butter melted, I added garlic (1 small glove, finely chopped). When the garlic became fragrant (1 minute), I added the nagaimo rounds and fried both sides (1-2 minutes each). I then put in the octopus and sauteed for another 1 minute. I added salt (1/3 tsp) melted in warm water (2 tbs) and mirin (2 tbs). I braised it until the liquid is almost all evaporated. I garnished with a very small pat of butter, perilla and freshly cracked white pepper (my additions).
This is an interesting dish. The nagaimo is still a bit slimy and may not be suitable for those with slimonphobia out there but is nicely crunchy with a buttery flavor. The octopus is rather tender (relative to other cooked octopi) and nice garlic taste. Perfect drinking snack for sake.