Combine eggs, honey, milk, and sugar in a mixing bowl, and whisk the mixture vigorously until it turns pale and creamy.
Add cake flour (or all purpose flour) and baking powder to the egg mixture, mix until just combined (do not overmix).
Pass the batter through a fine mesh strainer to remove any lumps. Using a whisk, scoop up some batter and allow it to drip back into the mixing bowl. The batter should fall in a smooth, continuous stream, forming a thin, straight line in the air. If the batter drips intermittently, you may need to add some extra milk (1 tsp at a time) to achieve the right consistency so that it drips continuously in a straight line. You may transfer the dorayaki batter to a sport cap bottle using a funnel, which can make it more convenient to pour the batter onto the frying pan. However, this step is optional. After preparing the batter, refrigerate it for 30 minutes to allow it to rest. While the dorayaki batter is resting, you may choose to prepare the mochi filling as an option. Traditional dorayaki is typically filled with red bean paste, but you can omit the mochi filling if you prefer.
To make the mochi filling: Add milk, cornstarch, sugar, and glutinous rice flour in a bowl. Stir with a whisk until the mixture is smooth. Pass the mixture through a fine mesh strainer to remove any lumps. Cover the bowl with microwave-safe plastic food wrap, use a toothpick to poke about 12 holes on the food wrap. Microwave on 100% powder for 3 minutes (or steam the mixture over high heat for 30 minutes until fully cooked) – Stick a toothpick into the middle of the mochi dough and if it comes out clean, the dough is fully cooked.
Put 10g butter on the top of the cooked mochi dough. Use a spatula or spoon to stir the the mochi dough until the butter is fully absorbed by the dough.
The dough can be quite sticky while still hot, so it's best to avoid touching it with your hands. Cover the dough with plastic wrap and leave it aside until it is completely cooled to room temperature.
Fill a large pan (or your sink) with at least 3 inches of cold water before you begin cooking the pancakes. This will be used to cool down the hot frying pan during the cooking process.
Heat a nonstick frying pan over medium low heat for 2 minutes. (For reference, I set my stovetop to level 4 out of 10.)
To form the pancake, pour the batter from the bottle or a ⅓ cup measuring cup with a spout onto the center of the nonstick frying pan, creating a circle that is about 3 inches in diameter. Keep the bottle or cup centered above the pan without moving it around, and let the batter drip down in a straight line to naturally form the pancake. Cook over medium low heat until bubbles form on the surface, wait until 70% of the bubbles are broken, then flip over the pancake and cook the other side for 30 seconds.
Remove the pancake from the pan and let cool on a wire rack with the smooth side facing up. After cooking each pancake, place the bottom of the frying pan in the cold water for 30 seconds to cool it down. Dry the frying pan completely with a kitchen towel before continuing to make the remaining pancakes. This recipe yields approximately 6 pancakes, which will make 3 dorayakis. If you want to make more, you can double the recipe.
Now the mochi dough should have been cooled to room temperature. Knead the mochi dough by stretching and folding it for about 5 minutes, until you can pull it as long as your forearm (about 10 inches).
Divide the mochi dough into 3 equal portions. To prevent it from sticking, wrap a rolling pin with plastic food wrap. Use the rolling pin to flatten each portion into a circle that is the same size as the pancakes.
Spread a layer of red bean paste onto the ugly side of one pancake, cover with a sheet of flattened mochi filling, and top with another pancake to create a sandwich. Repeat with the remaining pancakes and filling.
Enjoy with hot tea.