Cut off a one-third length section of a medium-sized bitter gourd (or roughly 100 gm) and cut in half, length-wise. Scrape out the seeds using a spoon. Slice into 5-mm slices. Place in a mixing bowl.
To reduce bitterness, sprinkle some salt. Rub salt into the slices, or toss several times to mix in evenly. Set aside for 10 minutes. Rinse slices under running water to rid of excess salt. Drain and set aside.
In a clean mixing bowl, combine light soy sauce, sesame oil, salt and white pepper. Stir with a spoon until well mixed. Break in the eggs. Lightly beat with a fork or whisk, until the eggs and seasonings are well combined.
Heat up a wok over high heat until hot. Add 1 tbsp oil. Stir fry bitter gourd slices until softened, about 1 minute, or when bitter gourd turns slightly translucent. Spread out the slices evenly, then drizzle all over with the remaining 1 tbsp of oil.
Beat or whisk the egg mixture one more time (to incorporate more air), then pour over slices, covering the edges and centre evenly. Once the edges of the omelette start to set, reduce to medium heat. (do not press down on the omelette as it cooks). Once the underside of the omelette has set firmly enough, flip over and let omelette cook through. Turn out onto a serving plate. Garnish with some Chinese coriander, and serve immediately.