Boil your noodles just short of al dente (you will finish them in the pan), rinse in cold water and set aside. In a large pan over high heat, add 2 tbsp oil, garlic and onions, and cook for 2 minutes. Add the rest of the vegetables and cook until they are almost soft but still yielding a crunch (about 8 minutes). Lower the heat and add noodles, water, soy sauce, sake, rice vinegar, sugar and nori. Mix well and cook for a couple of minutes.
While the veggies are finishing up in the pan, grab another pan to make your omelets. Use 2 eggs per omelet (break in a bowl and briefly whisk). Add oil to the pan and when the oil is hot, make your first omelet. When the omelet is ready, put it on a plate and repeat the process until all your omelets are made.
Equally divide the veggie and noodle mix and spread it on one side of each omelet. Fold with the empty side, squirt a good amount of Tonkatsu sauce on top, add some kewpie mayonnaise too if you like to add creaminess, and serve!