In a large pot, add 4 cups water, ½ tsp salt, and 2 Tbsp sake and bring it to boil.
Cut the green onions to thirds and cut the ginger into thin slices (you can keep the peel on). Add them to the pot.
Butterfly the chicken breast, by cutting the length of the side of the chicken breast with the edge of your knife parallel to the cutting board. Carefully slice the breast in half widthwise until the other edge. Now you have two pieces of chicken breast.
Once water is boiling, put the chicken in the pot. Cover the lid and reduce the heat to the lowest setting. Cook the chicken for 15 minutes, or until cooked through.
After cooking the chicken for 15 minutes, transfer it from the pot to a plate. Cover with plastic wrap to keep the moisture and let cool.
Prepare Honey Sesame Sauce
Toast 2 Tbsp sesame seeds in a frying pan (without oil) until fragrant, it will take from 3-5 minutes, depending on the heat. Swirl the pan once in a while to rotate the seeds.
Transfer the toasted sesame seeds into your Japanese mortar and pestle. You don’t have to completely grind the sesame seeds. To add texture to the dressing, it’s nice to keep both powdered sesame seeds and whole sesame seeds. If you don’t have a Japanese mortar and pestle, you can use a food processor.
Transfer the ground sesame seeds into a 2-cup measuring cup. Add honey, rice vinegar, soy sauce, and sesame oil. Whisk all together and set aside.
Prepare the toppings
Crack the eggs in a medium bowl and whisk well. Add ¼ tsp kosher salt and combine well.
Heat the oil in the non-stick frying pan over medium high heat. Once the frying pan is hot, add the egg mixture. Turn down the heat to low and swirl the pan to evenly distribute the egg in the pan. Once the egg mixture is set, you can flip to cook other side (optional) or continue to cook longer until the egg is cooked through. Turn off the heat and transfer the egg crepe to the working surface.
Cut the egg crepe in half and thinly slice it. Set aside.
Peel the cucumber but leave some strips not peeled (it looks better that way). Cut the cucumber diagonally into 1/8 inch slices. Then cut into thin long sticks. Set aside.
Cut the tomato in half and cut the each half into 3-4 wedges. Set aside.
Shred the chicken into thin long strips. When ingredients are in the same shape, it’s easier to combine with noodles and you can eat all the ingredients together.
Prepare the shirataki noodles
Boil 4 cups water in a saucepan for the shirataki noodle. Boiling shirataki noodles remove unwanted smell from the shirataki noodles, so don’t skip.
Open the package of shirataki noodles and drain. Rinse quickly under cold running water.
Once the water is boiling, add the shirataki noodles and cook for 2 minutes. Drain immediately and soak in iced bath.
Assemble the noodles
When the shirataki noodles are cold, drain well. On a plate, serve the shirataki noodles and toppings of your choice. Garnish with cilantro and drizzle the dressing.