Combine eggs, salt, and pepper together in a bowl.
Heat a few drops of oil in a skillet over medium-high heat. Add bean sprouts, shrimp, green onion, celery, and ginger; cook and stir until celery is translucent but still crisp, 3 to 4 minutes. Remove from heat, cool slightly, and stir into egg mixture.
Heat remaining oil in skillet over medium heat. Pour 1/4 egg-shrimp mixture into skillet; tilt pan to spread mixture evenly. Cook until golden brown, 1 to 3 minutes per side. Repeat with remaining egg-shrimp mixture.