Place tofu in a mixing bowl and crumble into small pieces with your hands or a fork. Add nagaimo or water (depending on which version you are making), mix, then add cabbage and ginger. Mix in any other add-ins you want.
Sprinkle in salt, baking powder, and flour/potato starch. Mix until well combined and everything is coated in batter.
Heat some oil in a pan over medium low heat, just enough to lightly coat the pan. Scoop some of the batter into the pan and tightly pack it into a circle. The batter will be loose at first, so pack it tightly and it will stick together once cooked. Make small pancakes for easier flipping.
Cook until browned on bottom and the edges start to dry, about 5 minutes (adjust heat if necessary). Then carefully flip the pancake over and cook another 5 minutes. Transfer to a plate and repeat until you use up the batter (you can cook multiple at once if you have a large pan).
Mix together the sauce ingredients (if making your own) and brush each okonomiyaki with sauce. Drizzle with mayonnaise and sprinkle aonori on top to serve.