Prepare your takoyaki pan by preheating it over medium-high heat until very hot (around 180°C/350°F). While waiting, mix 1 cup takoyaki flour, 450ml water, and 1 medium egg in a bowl until smooth with no lumps. Pour this batter into a squeeze bottle or pitcher with a spout for easy pouring.
Once the pan is hot, brush each mold generously with oil. Fill each mold to the brim with batter. Quickly add one piece of cubed octopus (or your chosen filling) and sprinkle tempura crumbs into each mold.
Let the batter cook for about 2 minutes until you see bubbles forming and the bottom turning golden brown. Using a bamboo skewer or pick, gently scrape around the edges of each ball, then push the pick into the middle and flip each one about 90 degrees. Add a little more batter to fill any gaps.
Continue cooking and turning the balls every minute or so, adding small amounts of batter as needed to fill holes, until they form perfect golden-brown spheres. This usually takes about 5-6 minutes total. You'll know they're done when they can rotate freely and have an even, golden-brown color all around.
Transfer the finished balls to a serving plate using your picks. Top with takoyaki sauce and Japanese mayonnaise in a zig-zag pattern. Sprinkle with bonito flakes, aonori (seaweed), and chopped green onions. For extra indulgence, add sliced cheese and melt it quickly with a kitchen torch or under the broiler for a minute.
For the homemade sauce, combine minced garlic, minced ginger, honey, oyster sauce, tomato sauce, Worcestershire sauce, and mentsuyu in a small pan. Cook over low heat, stirring occasionally, until the sauce thickens slightly. Let it cool before using.
Serve your takoyaki immediately while hot and crispy. Each batch makes about 32 balls, enough for 4-6 people to enjoy as a snack or appetizer.