In a mixing bowl, combine the bean sprouts, shrimp, eggs, mushrooms, scallions and 1/2 teaspoon of salt.
Mix thoroughly.
Heat a deep skillet over high heat until 1 or 2 drops of water bubble when sprinkled in.
Add oil and turn heat back to Medium-High.
Pour in 1/2 cup of egg mixture into pan. Push cooked egg up over shrimp with a spatula to form a patty. Fry until golden brown, turning once, about 4 minutes.
Repeat with remaining egg mixture. If you need to, add more oil. Keep patties warm.
In a saucepan over medium heat, combine chicken broth, soy sauce, 1/4 teaspoon salt and white pepper to taste. Bring to a boil.
Mix cornstarch and water; stir into broth mix. Cook and stir until thickened (about 10 seconds).