Make batter: In a large mixing bowl, whisk together applesauce, soy milk, oil, and sugar. Sift in cake flour, baking powder, and baking soda and whisk until just combined.
Rest batter: Cover and batter refrigerate for 30 minutes.
Heat pan: Place a taiyaki pan over the stove on medium heat. Brush both sides of the pan with oil. Heat each side of the pan for about 2 minutes.
Add batter: Spoon batter into the molds on one side (the side placed on the stove). Spread the batter a bit so a thin layer covers the entire mold. Place a tablespoon of anko in the middle, then pour batter on top to cover.Tip: The batter will spread and rise a bit once you close the lid, so be careful not to overfill or the batter will spill out.
Cook: Close the lid of the pan and cook for about 2 minutes or until browned. Then flip and cook the other side another 2 minutes or until browned.Tip: You may need to adjust the heat of the stove if your taiyaki is browning too quickly or not browning enough. Use the first taiyaki as a test and adjust as you go.
Repeat: Carefully remove each taiyaki from the pan, close the lid, and let the pan reheat for about a minute on each side. Then repeat the cooking process until all the batter is used up.
Taiyaki is best served warm right after making. I like to wrap mine in a kitchen towel to keep warm while I make the rest, but this will make the outside softer. If you want your taiyaki to be more crisp, you can place them on a wire rack, but they will cool down more quickly and dry out if you don't eat them soon.
Notes
You will need a special taiyaki pan to make this. I used this one* from Amazon.1) If you don't have cake flour, you can use 132 grams all purpose flour + 18 grams cornstarch.