Coat: Place the steak strips in a bowl and add the cornflour, salt, and pepper. Toss together until the beef strips are completely coated.
Crisp: Heat the oil in a wok or large frying pan over high heat. Add the beef and fry until dark brown and crispy, about 5 minutes. Remove the beef with a slotted spoon and place it in a bowl lined with kitchen roll to soak up excess fat.
Stir-fry: Reduce the heat to medium and add another tablespoon of oil to the wok. Add the broccoli and red pepper and stir-fry for 2-3 minutes until lightly cooked but still crisp. Add the garlic and ginger, and fry for another 30 seconds.
Sauce: In a bowl, combine lime juice, soy sauce, sugar, and chopped chilli. Stir together and pour the sauce into the wok. Turn the heat to high and let the sauce bubble for 2-3 minutes until reduced by about one-third.
Noodles: Add the noodles to the wok and cook, tossing regularly with tongs, until heated through, about 2-3 minutes.
Combine: Add the cooked beef, broccoli, peppers, and spring onions back to the wok. Heat through for 2-3 minutes, tossing to prevent sticking.
Serve: Dish out into bowls and top with chilli flakes, chopped chillies, and spring onions.