Trim excess fat from beef and cut into big pieces. Brown beef in batches. Fry onion, garlic, add tomato paste, deglaze with water. Return beef to the pan.
Add zest and juice of oranges, lime juice, chilis, salt, and pepper. Braise covered for 4-5 hours, checking occasionally and adding water if needed.
Roast carrots tossed with oil, salt, and pepper until golden. Add lime zest before serving.
Boil egg noodles, then toss with butter.
Remove chilis from the beef. Adjust sauce seasoning. Stir in egg yolks off heat, then simmer to thicken the sauce. Add beef back to coat with the sauce. Add herbs and water if needed.
Serve beef with carrots and egg noodles.
Notes
Reheat gently to avoid overcooking the egg in the sauce.