Heat 1 tablespoon oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add shrimp in even layer and cook without moving until browned on bottom, about 90 seconds. Stir and continue to cook until just cooked through, about 90 seconds. Push shrimp to sides of skillet. Add 1 tablespoon oil to center, then add eggs. Using rubber spatula, stir eggs gently and cook until set but still wet, about 1 minute. Stir eggs into shrimp and continue to cook, breaking up large pieces of egg, until eggs are fully cooked, about 30 seconds. Transfer shrimp-egg mixture to bowl.

Heat 1 tablespoon oil in now-empty skillet over medium heat until shimmering. Add bell pepper and cook until crisp-tender, about 2 minutes. Stir in scallion whites and ginger and cook until fragrant, about 30 seconds; transfer to bowl with shrimp.

Return now-empty skillet to medium-high heat, and heat remaining 2 tablespoons oil, curry powder, and cayenne, if using, stirring occasionally, until fragrant, about 2 minutes. Off heat, add chicken broth and soy sauce. Return to medium-high heat and bring to simmer. Add noodles and cook, stirring frequently, until liquid is absorbed, 5 to 7 minutes. Add shrimp and vegetable mixture and toss to combine. Add bean sprouts, scallion greens, and lime juice, and toss to combine. Serve immediately.