Bring a medium pan of water to the boil. Add the noodles and cook for 3 minutes until tender. Drain and set aside.
Heat the oil in a large wok or frying pan. Add the onion and stir-fry for 2-3 minutes, until beginning to soften. Add the chilli, garlic and paste and stir-fry for a further minute.
Add the peppers, carrot and broccoli to the wok and stir-fry for 3 minutes, until just tender.
Add the leftover roast beef to the wok along with the cooked and drained egg noodles, soy sauce and 100ml of water. Heat through, stirring, then divide between 4 bowls and serve immediately.