In a large bowl, whisk together 1 2/3 cups all-purpose flour, 3 1/3 cups dashi stock, 1 large egg, 1 teaspoon soy sauce, and a pinch of salt until smooth and lump-free.
Let the batter rest for 15 to 20 minutes so the flour fully hydrates.
Meanwhile, cut about 7 ounces of cooked octopus into 1/2-inch pieces, thinly slice the green parts of 4 scallions, and measure out 1/4 cup tempura scraps (tenkasu).
Heat a takoyaki pan or an aebleskiver pan over medium-high heat, and brush each cavity generously with vegetable oil.
Pour the batter into each cavity, filling it nearly to the top, then add one piece of octopus, some scallions, and a few tempura scraps to each.
After 2 to 3 minutes, when the edges start to set and brown, use skewers or chopsticks to rotate each piece a quarter turn so it begins to form a round ball.
Continue rotating the takoyaki for another 5 to 7 minutes, cooking until they're evenly golden brown and crispy on the outside.
Transfer the takoyaki to a plate, drizzle with takoyaki sauce and Japanese mayonnaise, sprinkle with bonito flakes and aonori, and serve immediately.