Cut the octopus into bite-sized pieces, about 0.4 inch (1cm) wide. Thinly slice the green onions. Finely chop the beni shoga.
Crack the egg into a large bowl and beat it. In the bowl, add sugar, salt, soy sauce, dashi, and baking powder, and mix everything together. Next, gradually add flour in multiple portions, whisking thoroughly each time to prevent lumps from forming. The takoyaki batter is ready.
Preheat the takoyaki maker to high heat (392°F/200°C or above). Pour oil into a small bowl and soak 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 comes out from the takoyaki maker, pour the takoyaki batter into each cavity. Next, add chopped octopus to each cavity. It's okay if the takoyaki batter overflows from the cavities during this process.
Then, sprinkle the tenkasu, green onions, and beni shoga evenly over each cavity. Wait until the batter on the side walls of each cavity set.
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 batter 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.
Turn each ball over to brown them evenly. If you want to keep them warm in the takoyaki maker, set it to a very low temperature.
Serve them on each individual plate. If you enjoy them with sauce, top each takoyaki with takoyaki sauce, Japanese mayonnaise, aonori, and bonito flakes according to your preference.