Cut bitter gourd in half lengthwise. Scoop out the seeds with a spoon. Cut one half of the bitter gourd at a diagonal into thin slices. Do the same for the other half.
Place the bitter gourd slices in a bowl. Sprinkle 1 teaspoon salt over the top. Mix well and allow it to sit for 20 minutes. Rinse and squeeze out as much water as possible. Pat dry with paper towel.
Heat vegetable oil in a wok or medium fry pan. Add prepared bitter gourd and stir fry for 3 minutes until lightly brown.
Pour in the beaten egg. Sprinkle salt and ground pepper over the eggs and bitter gourd.
Once eggs start to set, stir to break it up. Continue stirring and flipping until eggs are fully cooked, about 3 minutes.