For the beef, pour the vegetable oil into a deep fat fryer or medium saucepan and heat until it reaches 180C/350F, or when a small cube of bread dropped in turns golden in 30 seconds. (NB: Hot oil can be dangerous. Do not leave unattended.)
Whisk the eggs, cornflour and salt in a bowl to a thick batter.
Coat the steak strips in the batter, shaking off any excess, and fry for two minutes in the oil, or until just crisp and turning golden-brown. Remove with a slotted spoon and set aside on kitchen paper. Coat the carrot strips in the batter, shaking off any excess, and fry for two minutes in the oil, or until just crisp and turning golden-brown. Remove with a slotted spoon and set aside on kitchen paper.
Heat a wok with one tablespoon of the deep-frying oil. Add the spring onions, ginger, garlic and chilli and stir-fry for one minute.
Add the sugar, vinegar and soy sauce, deep-fried beef and carrots and stir until well combined. Remove the pan from the heat.
Serve the chilli beef with boiled rice, chilli slices and lime wedges.