In a mixing bowl, whisk together the eggs, soy sauce, sesame oil, salt, and black pepper until well combined.
Stir in the bean sprouts, green onions, bell pepper, and cooked shrimp or chicken if using. Mix until evenly distributed.
Heat 1 tablespoon of vegetable oil in a non-stick skillet over medium heat.
Pour half of the egg mixture into the skillet, spreading it evenly. Cook for about 3-4 minutes or until the edges start to set and the bottom is golden brown.
Carefully flip the omelette and cook for an additional 2-3 minutes until fully cooked through. Remove from the skillet and keep warm.
Repeat the process with the remaining egg mixture, adding more oil if necessary.
Serve hot, garnished with additional green onions if desired.