In a saucepan over medium heat, cook instant noodles 1 to 2 minutes shy of package directions. Drain well, reserving about 2 tablespoons of the liquid. Keep warm.
In a small bowl, combine the reserved liquid, Srichacha, soy sauce, and brown sugar. Stir until well combined and sugar is dissolved. Set aside.
In a wok or wide pan over medium heat, heat 1 tablespoon of the oil. Add eggs and cook, breaking into pieces, until set but still moist. Remove from wok and keep warm
Heat another 1 tablespoon of oil. Add shrimps and cook just until color changes. Remove from pan and keep warm.
Wipe down with paper towels, if needed. Heat the remaining 1 tablespoon oil. Add onions and garlic and cook until softened.
Add chicken and cook until color changes and is cooked through.
Add carrots and cook until half done.
Add cabbage and continue to cook for about 1 minute.
Add noodles, shrimp, and sauce. Gently toss to combine and distribute sauce.
Add eggs and bean sprouts. Continue to cook, tossing gently, for about 1 to 2 minutes or until noodles are heated through and vegetables are tender yet crisp.
Divide onto serving plates. Sprinkle with red pepper flakes, if desired. Garnish with green onions and serve with lemon or lime wedges.