Heat sesame oil and butter in a large saucepan over medium heat until butter melts completely, about 1 minute.
Add minced garlic and ginger, frying for 1 minute while stirring constantly to prevent burning. Garlic should turn light golden, not brown.
Add chicken stock, light soy sauce, dark soy sauce, sriracha, Chinese rice wine, brown sugar, and white pepper. Stir together until sugar dissolves, then add shredded cooked chicken breast.
Turn heat to high and bring to a rolling boil, then reduce to simmer for 3 minutes to heat chicken through to 165°F.
Add instant noodles to simmering broth, ensuring broth covers noodles by at least 1 inch. Bring back to a boil, then simmer for 3 minutes, stirring occasionally to separate noodles.
Use tongs to divide noodles between four bowls. Ladle broth and chicken pieces over noodles.
Top each bowl with spring onions, 2 egg halves, carrot strips, sesame seeds, and optional chilli oil. Serve immediately.
Notes
Prep time assumes eggs are already cooked and chicken is already shredded. Add 15 minutes for soft-boiling eggs and 5 minutes for shredding chicken if starting from scratch.
Chinese rice wine adds essential depth to the broth. Dry sherry is an excellent substitute if unavailable.
Use both light and dark soy sauce for balanced flavor and rich color. Can substitute with low-sodium versions if broth tastes too salty.
Instant noodles cook quickly and have nice texture. Can swap for dried ramen, rice noodles, or soba noodles with adjusted cooking times.
Store broth and noodles separately in refrigerator for best results when reheating. Reheat broth to at least 165°F for food safety.