Cut octopus into bite-sized pieces, about ⅖ inch (1cm) wide. Thinly slice green onions. Finely chop beni shoga.
Crack egg into a large bowl and beat it. Add sugar, salt, soy sauce, chilled dashi, and baking powder to the bowl, and mix everything together. Then, gradually add flour in multiple portions, whisking thoroughly each time to prevent lumps from forming. The takoyaki batter is ready.
Preheat a takoyaki maker to high heat (392℉/200℃ or above). Pour oil into a small bowl and soak the tip of a folded paper towel in it. Use the soaked towel to thoroughly coat all of the cavities and the flat surface on top of the takoyaki maker with oil.
When smoke starts to come out from the takoyaki maker, pour the takoyaki batter into each cavity, then add the chopped octopus to each cavity. It's fine if the takoyaki batter overflows from the cavities during this process.
Sprinkle tenkasu, green onions, and beni shoga evenly over each cavity. Wait until the batter on the side walls of each cavity sets.
Cut the batter on the top flat surface between each cavity using a takoyaki pick or skewer. Then, flip the cooked portion of each cavity over about 90 degrees (a quarter turn).* Wait again until the uncooked portion of the batter is cooked through.* If the batter on the side walls has set, you can flip it over by applying a bit of force with the pick or skewer. If it doesn't flip, cook it for a little longer. It doesn't matter if the batter tears slightly. Flip the cooked portion over an additional 90 degrees to cook the remaining uncooked portion.
Since the takoyaki maker might cook differently depending on the position of the cavities, if there are any lightly cooked balls, replace them with well-cooked ones. Then, turn each ball over to brown them evenly.
Serve them on individual plates. If you enjoy them with sauce, top each takoyaki with takoyaki sauce, Japanese mayonnaise, aonori, and bonito flakes to taste.