In a large mixing bowl, whisk together 4 large beaten eggs with red bell pepper, celery, mushrooms, onion, and bean sprouts. Add half of the chopped scallions, kosher salt, and white pepper to taste. Allow the mixture to sit for about 5 minutes.

In a medium saucepan, combine chicken broth, soy sauce, rice vinegar, and brown sugar over low heat. Stirring continuously, bring to a gentle simmer. Mix cornstarch with cold water to create a slurry and whisk it into the sauce, cooking until it thickens and bubbles—about 3-5 minutes.

Heat canola oil in a skillet over medium heat until shimmering. Pour in 1/2 cup of the egg mixture, cook for 3-4 minutes until golden brown on the bottom. Carefully flip and cook for an additional 2-3 minutes.

Repeat with the remaining egg mixture, adding more oil as needed, cooking each omelet until golden and fluffy.

Plate the omelets while warm, drizzle the gravy over the top, and garnish with the remaining scallions.