Start by making the sauce. In a mixing bowl, combine the hot water and 3 tablespoons of sugar. Whisk until the sugar dissolves completely.
Add in the soy sauce, vinegar, sesame oil, and chili oil if you desire. Whisk to combine. Then cover and refrigerate until serving time.
Next, make the omelet strips. Whisk the eggs, sugar, and water together until well combined.
In a nonstick frying pan, heat the vegetable oil over high heat until shimmering.
Pour in the egg mixture and quickly turn the pan to coat the bottom. Cook for 1-2 minutes until the top is set.
Once the top of the egg is set, flip it over and cook the other side for another 1 minute or so until cooked. Remove from heat and set aside to cool. Pat a paper towel on it to absorb any extra oil.
While the omelet is cooling, diagonally slice the cucumber so you have elongated oval slices. Then, finely julienne those oval slices to get thin strips. Set side.
Lay the ham slices so they are stacked together. Finely julienne the ham into thin strips.
Thinly slice the cooled omelet into julienne slices.
Bring a pot of water to a boil. Add the ramen noodles and separate them in the water using chopsticks or tongs. Cook for 2 minutes if using fresh, and 3 minutes if using dried. (I normally will take them off the heat in the last minute- they cook very fast!)
Drain the noodles in a colander and immediately rinse with cold running water. (Tip: I like to prepare a bowl of ice-water to dip my rinsed noodles in- totally optional but it chills them faster!)
Divide the drained noodles among serving dishes. Arrange the toppings on top of the noodles and garnish with the pickled ginger and toasted sesame seeds if desired. Serve with the chilled chuka dressing on the side. Enjoy!