1. Combine all the sauce ingredients in a small saucepan and simmer for 30 seconds, stirring constantly. Remove from the heat and cool to room temperature.

2. Beat the eggs in a large bowl. Add the flour and water and continue beating until you have a batter the consistency of pancake batter. Add the sake. Fold in the cabbage and scallions. Be sure to mix the batter and vegetables together evenly. Each okonomiyaki will use 1/2 of the mixture.

3. Heat 1 tablespoon of the oil in a standard 10-inch skillet. Spoon 1/2 of the batter onto the hot skillet (like a pancake) making sure the vegetables are evenly distributed. Then sprinkle 1/2 of whatever other ingredients you have on top. Cook each side on medium heat for 2 minutes until lightly browned. Reduce the heat to low and cook, covered for another 5 minutes, occasionally turning and gently pressing the okonomiyaki with a spatula. Prepare the other okonomiyaki as above. Keep the finished pancakes warm in a low oven while making the rest, or use two skillets and make two okonomiyaki at a time.

4. Serve immediately topped with the sauce or with mayonaise.