In a large pan, heat a tablespoon of oil over medium-high heat. Add the beef mince and cook until browned, stirring occasionally, for about 5-7 minutes.
Add the onion and garlic to the pan, and continue cooking until the onion is softened, for about 2-3 minutes.
Add the grated carrot and sliced cabbage to the pan, and stir-fry for another 2-3 minutes, or until the vegetables are just tender.
Add the soy sauce, oyster sauce, brown sugar and black pepper to the pan, and stir until well combined. Cook for another 1-2 minutes, or until the mixture is heated through.
Remove the pan from the heat and allow the mixture to cool to room temperature.
To assemble the lumpia, place a spring roll wrapper on a flat surface, with one corner facing towards you. Spoon a tablespoon of the beef mixture onto the wrapper, spreading it out in a thin line, leaving about 2cm of space from the edges.
Fold the corner nearest to you over the filling, and then fold in the sides. Roll the wrapper up tightly, brushing the remaining corner with beaten egg to seal it.
Repeat the process with the remaining spring roll wrappers and filling.
In a deep frying pan or wok, heat enough oil to deep fry the lumpia until golden brown, for about 3-4 minutes. Drain on kitchen paper.
Serve the beef lumpia hot with sweet chilli sauce or your preferred dipping sauce.